Vacuolar ATPases (V‐ATPases, V1Vo‐ATPases) are rotary motor proton pumps that acidify intracellular compartments, and, when localized to the plasma membrane, the extracellular space. V‐ATPase is regulated by a unique process referred to as reversible disassembly, wherein V1‐ATPase disengages from Vo proton channel in response to diverse environmental signals. Whereas the disassembly step of this process is ATP dependent, the (re)assembly step is not, but requires the action of a heterotrimeric chaperone referred to as the RAVE complex. Recently, an (...) alternative pathway of holoenzyme disassembly was discovered that involves binding of Oxidation Resistance 1 (Oxr1p), a poorly characterized protein implicated in oxidative stress response. Unlike conventional reversible disassembly, which depends on enzyme activity, Oxr1p induced dissociation can occur in absence of ATP. Yeast Oxr1p belongs to the family of TLDc domain containing proteins that are conserved from yeast to mammals, and have been implicated in V‐ATPase function in a variety of tissues. This brief perspective summarizes what we know about the molecular mechanisms governing both reversible (ATP dependent) and Oxr1p driven (ATP independent) V‐ATPase dissociation into autoinhibited V1 and Vo subcomplexes. (shrink)

Master Nikon's first mirrorless camera with this full-color guide The Nikon 1 is a revolutionary new pocket-size camera line that packs the power of a digital SLR into a smaller body. This easy-to-follow guide covers both the J1 and V1 models, showing you all the modes and capabilities of each and how to use them. Illustrated with full-color images to show what you can achieve, it explores all the controls, different lenses, auto and video shooting modes, and how you can (...) take creative control of your photos. It also teaches you which format to use, how to organize and manage your images, and how to get super shots of people, landscapes, action, and more. This guide by leading photography instructor Julie Adair King provides a complete introduction to using the new Nikon 1 J1 and V1 models Covers all the camera controls and how to use them, lenses, auto and video modes, and how to take control of exposure, color, and lighting Explains how to get images from the camera to the computer, manage your photo files, and make basic edits Full-color illustrations show the great effects you can achieve Nikon 1 J1/V1 For Dummieshelps you get the most from Nikon's new mirrorless camera. (shrink)

The human brain’s ongoing activity is characterized by intrinsic networks of coherent fluctuations, measured for example with correlated functional magnetic resonance imaging signals. So far, however, the brain processes underlying this ongoing blood oxygenation level dependent (BOLD) signal orchestration and their direct relevance for human behavior are not sufficiently understood. In this study, we address the question of whether and how ongoing BOLD activity within intrinsic occipital networks impacts on conscious visual perception. To this end, backwardly masked targets were presented (...) in participants’ left visual field only, leaving the ipsi-lateral occipital areas entirely free from direct effects of task throughout the experiment. Signal time courses of ipsi-lateral BOLD fluctuations in visual areas V1 and V2 were then used as proxies for the ongoing contra-lateral BOLD activity within the bilateral networks. Magnitude and phase of these fluctuations were compared in trials with and without conscious visual perception, operationalized by means of subjective confidence ratings. Our results show that ipsilateral BOLD magnitudes in V1 were significantly higher at times of peak response when the target was perceived consciously. A significant difference between conscious and non-conscious perception with regard to the pre-target phase of an intrinsic-frequency regime suggests that ongoing V1 fluctuations exert a decisive impact on the access to consciousness already before stimulation. Both effects were absent in V2. These results thus support the notion that ongoing slow BOLD activity within intrinsic networks covering V1 represents localized processes that modulate the degree of readiness for the emergence of visual consciousness. (shrink)

A novel class of proton‐ATPase has been identified in the vacuolar system of eukaryotic cells. The properties of these enzymes and their relation to other proton‐ATPases is discussed.

A key question in understanding visual awareness is whether any single cortical area is indispensable. In a transcranial magnetic stimulation experiment, we show that observers' awareness of activity in extrastriate area VS depends on the amount of activity in striate cortex (Vl). From the timing and pattern of effects, we infer that back-projections from extrastriate cortex influence information content in Vl, but it is Vl that determines whether that information reaches awareness.

A fast growing family of ATPases has recently been highlighted. It was named the AAA family, for ATPases Associated to a variety of cellular Activities. The key feature of the family is a highly conserved module of 230 amino acids present in one or two copies in each protein. Despite extensive sequence conservation, the members of the family fulfil a large diversity of cellular functions: cell cycle regulation, gene expression in yeast and HIV, vesicle‐mediated transport, peroxisome assembly, 26S protease function (...) etc. In addition, several members of this family can be found in the same organism (up to 17 in S. cerevisiae). The contrast between functional diversity and structural conservation of the module, from archaebacteria to mammals, suggests that it plays an essential, but as yet unknown, role at key points of the cellular machinery. Two (non‐exclusive) such possibilities are: (1) ATP‐dependent proteasome function and (2) ATP‐dependent anchorage of proteins. Finally, the basic biochemical activity of the AAA module is still a matter of speculation, and we propose that it acts as an ATP‐dependent protein clamp. (shrink)

We present a neuro-geometrical model for generating the shape of Kanizsa's modal subjective contours which is based on the functional architecture of the primary areas of the visual cortex. We focus on V1 and its pinwheel structure and model it as a discrete approximation of a continuous fibration π: R × P → P with base space the space of the retina R and fiber the projective line P of the orientations of the plane. The horizontal cortico-cortical connections of V1 (...) implement what the geometers call the contact structure of the fibration π, and defines therefore an integrability condition which can be shown to correspond to Field's, Hayes', and Hess' psychophysical concept of association field. We present then a variational model of curved modal illusory contours based on the idea that virtual contours are “geodetic” integral curves of the contact structure. (shrink)

This collection of essays showcases the most important and influential philosophical works of the ancient and medieval period, roughly from 600 BC to AD 1600. Each chapter takes a particular work of philosophy and discusses its proponent, its content and central arguments. These are: Plato's Republic; Aristotle' Nichomachean Ethics; Lucretius' On the Nature of the Universe; Sextus Emperiicus' Outlines of Pyrrhonism; Plotinus' The Enneads; Augustine's City of God; Anselm's Proslogion; Aquinas' Summa Theologia; Duns Scotus' Ordinatio; William of Ockham's Summa Logicae.

Clp ATPase chaperone proteins are found in procaryotes and eucaryotes. Recently, ClpC of Bacillus subtilis was found to be part of a regulatory switch(1). ClpC, in combination with the MecA and ComS proteins, regulates the activity of a transcription factor, ComK, which is necessary for the development of genetic competence (the ability to bind and take up exogenous DNA). The complex of ClpC:MecA:ComK renders ComK inactive. Interaction between ComS and the ternary complex releases active ComK. This regulatory switch controls (...) ComK activity in response to cell density signals that affect production of ComS. Regulated interaction between Clp ATPases and target proteins might prove to be widespread. (shrink)

The extent to which visual processing can proceed in the visual hierarchy without awareness determines the magnitude of perceptual delay. Increasing data demonstrate that primary visual cortex (V1) is involved in consciousness, constraining the magnitude of visual delay. This makes it possible that visual delay is actually within the optimal lengths to allow sufficient computation; thus it might be unnecessary to compensate for visual delay.

Ca2+ transients in myocardial cells are modulated by cyclic AMP‐dependent phosphorylation of a protein in the sarcoplasmic reticulum. This protein, termed phospholamban, serves to regulate the Ca2+ pump ATPase of this membrane, thus altering the mode of Ca2+ transients and the myocardial contractile response. Elucidating the structure of phospholamban and its intimate interaction with the Ca2+ pump ATPase should provide the basis for understanding, at the molecular level, how the cAMP system contributes to excitation‐contraction coupling in muscle cells.

Adenosine triphosphate, ATP, is the energy currency of living cells. While ATP synthases of archae and ATP synthases of pro‐ and eukaryotic organisms operate as energy producers by synthesizing ATP, the eukaryotic V‐ATPase hydrolyzes ATP and thus functions as energy transducer. These enzymes share features like the hydrophilic catalytic‐ and the membrane‐embedded ion‐translocating sector, allowing them to operate as nano‐motors and to transform the transmembrane electrochemical ion gradient into ATP or vice versa. Since archaea are rooted close to the (...) origin of life, the A‐ATP synthase is probably more similar in its composition and function to the “original” enzyme, invented by Nature billion years ago. On the contrary, the V‐ATPases have acquired specific structural, functional and regulatory features during evolution. This review will summarize the current knowledge on the structure, mechanism and regulation of A‐ATP synthases and V‐ATPases. The importance of V‐ATPase in pathophysiology of diseases will be discussed. BioEssays 30:1096–1109, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

This paper focuses on meditation as natural luminousity.

This paper describes the non dual relationship between the visible and the invisible.

The ring‐shaped ATPase machine, cohesin, regulates sister chromatid cohesion, transcription, and DNA repair by topologically entrapping DNA. Here, we propose a rigid scaffold model to explain how the cohesin regulators Pds5 and Wapl release cohesin from chromosomes. Recent studies have established the Smc3‐Scc1 interface as the DNA exit gate of cohesin, revealed a requirement for ATP hydrolysis in ring opening, suggested regulation of the cohesin ATPase activity by DNA and Smc3 acetylation, and provided insights into how Pds5 and (...) Wapl open this exit gate. We hypothesize that Pds5, Wapl, and SA1/2 form a rigid scaffold that docks on Scc1 and anchors the N‐terminal domain of Scc1 (Scc1N) to the Smc1 ATPase head. Relative movements between the Smc1‐3 ATPase heads driven by ATP and Wapl disrupt the Smc3‐Scc1 interface. Pds5 binds the dissociated Scc1N and prolongs this open state of cohesin, releasing DNA. We review the evidence supporting this model and suggest experiments that can further test its key principles. (shrink)

Attempts to solve the puzzling problem of oxidative phosphorylation led to four very different hypotheses each of which suggested a different view of the ATP synthase, the phosphorylating enzyme. During the 1960s and 1970s evidence began to accumulate which rendered Peter Mitchell’s chemiosmotic hypothesis, the novel part of which was the proton translocating ATP synthase (ATPase), a plausible explanation. The conformational hypothesis of Paul Boyer implied an enzyme where ATP synthesis was driven by the energy of conformational changes in (...) the respiratory proteins. This was finally abandoned as an explanation of the overall process. Nevertheless the conformational understanding of the enzyme became an acceptable proposal during the early 1970s and eventually led Boyer to a view of the enzyme that incorporated both hypotheses. The correspondence between Mitchell and Boyer, both Nobel laureates, exposes their different approaches to both this enzyme and to the hypotheses of oxidative phosphorylation and illuminates a key step in the development of bioenergetics. In particular Boyer was suspicious of proton gradients, because he could not envisage a chemical mechanism for the synthesis of ATP, while Mitchell distrusted conformational arguments because he believed the proton must act vectorially at the active site of the enzyme. This resulted in two different views of the mechanisms operating in this enzyme. Ultimately while Boyer was able to marry the two approaches, Mitchell retained his insistence on the role of the proton at the active site and was thus unable to give significance to Boyer’s conformational ideas. The underlying issues in this debate are discussed particularly with reference to the differing styles of Boyer and Mitchell and the influence of molecular biology, especially the development of protein technology. (shrink)

A model of face representation, inspired by the biology of the visual system, is compared to experimental data on the perception of facial similarity. The face representation model uses aggregate primary visual cortex (V1) cell responses topographically linked to a grid covering the face, allowing comparison of shape and texture at corresponding points in two facial images. When a set of relatively similar faces was used as stimuli, this Linked Aggregate Code (LAC) predicted human performance in similarity judgment experiments. When (...) faces of perceivable categories were used, dimensions such as apparent sex and race emerged from the LAC model without training. The dimensional structure of the LAC similarity measure for the mixed category task displayed some psychologically plausible features but also highlighted differences between the model and the human similarity judgements. The human judgements exhibited a racial perceptual bias that was not shared by the LAC model. The results suggest that the LAC based similarity measure may offer a fertile starting point for further modelling studies of face representation in higher visual areas, including studies of the development of biases in face perception. (shrink)

We consider two models V1, V2 of ZFC such that V1 ⊆ V2, the cofinality functions of V1 and of V2 coincide, V1 and V2 have that same hereditarily countable sets, and there is some uncountable set in V2 that is not covered by any set in V1 of the same cardinality. We show that under these assumptions there is an inner model of V2 with a measurable cardinal κ of Mitchell order κ++. This technical result allows us to show (...) that changing cardinal characteristics without changing cofinalities or ω-sequences has consistency strength at least Mitchell order κ++. From this we get that the changing of cardinal characteristics without changing cardinals or ω-sequences has consistency strength Mitchell order ω1, even in the case of characteristics that do not stem from a transitive relation. Hence the known forcing constructions for such a change have lowest possible consistency strength. We consider some stronger violations of covering which have appeared as intermediate steps in forcing constructions. (shrink)

Sarco/endoplasmic reticulum Ca2+ ATPase 2b (SERCA2b), a member of the SERCA family, is expressed ubiquitously and transports Ca2+ into the sarco/endoplasmic reticulum using the energy provided by ATP binding and hydrolysis. The crystal structure of SERCA2b in its Ca2+‐ and ATP‐bound (E1∙2Ca2+‐ATP) state and cryo‐electron microscopy (cryo‐EM) structures of the protein in its E1∙2Ca2+‐ATP and Ca2+‐unbound phosphorylated (E2P) states have provided essential insights into how the overall conformation and ATPase activity of SERCA2b is regulated by the transmembrane helix (...) 11 and the subsequent luminal extension loop, both of which are specific to this isoform. More recently, our cryo‐EM analysis has revealed that SERCA2b likely adopts open and closed conformations of the cytosolic domains in the Ca2+‐bound but ATP‐free (E1∙2Ca2+) state, and that the closed conformation represents a state immediately prior to ATP binding. This review article summarizes the unique mechanisms underlying the conformational and functional regulation of SERCA2b. (shrink)

Blindsight is classically defined as residual visual capacity, e.g., to detect and identify visual stimuli, in the total absence of perceptual awareness following lesions to V1. However, whereas most experiments have investigated what blindsight patients can and cannot do, the literature contains several, often contradictory, remarks about remaining visual experience. This review examines closer these remarks as well as experiments that directly approach the nature of possibly spared visual experiences in blindsight.

Visual imagery is a form of sensory imagination, involving subjective experiences typically described as similar to perception, but which occur in the absence of corresponding external stimuli. We used the Activation Likelihood Estimation algorithm (ALE) to identify regions consistently activated by visual imagery across 40 neuroimaging studies, the first such meta-analysis. We also employed a recently developed multi-modal parcellation of the human brain to attribute stereotactic co-ordinates to one of 180 anatomical regions, the first time this approach has been combined (...) with the ALE algorithm. We identified a total 634 foci, based on measurements from 464 participants. Our overall comparison identified activation in the superior parietal lobule, particularly in the left hemisphere, consistent with the proposed ‘top-down’ role for this brain region in imagery. Inferior premotor areas and the inferior frontal sulcus were reliably activated, a finding consistent with the prominent semantic demands made by many visual imagery tasks. We observed bilateral activation in several areas associated with the integration of eye movements and visual information, including the supplementary and cingulate eye fields (SCEFs) and the frontal eye fields (FEFs), suggesting that enactive processes are important in visual imagery. V1 was typically activated during visual imagery, even when participants have their eyes closed, consistent with influential depictive theories of visual imagery. Temporal lobe activation was restricted to area PH and regions of the fusiform gyrus, adjacent to the fusiform face complex (FFC). These results provide a secure foundation for future work to characterise in greater detail the functional contributions of specific areas to visual imagery. (shrink)

Despite thermodynamic, bioenergetic and phylogenetic failings, the 81‐year‐old concept of primordial soup remains central to mainstream thinking on the origin of life. But soup is homogeneous in pH and redox potential, and so has no capacity for energy coupling by chemiosmosis. Thermodynamic constraints make chemiosmosis strictly necessary for carbon and energy metabolism in all free‐living chemotrophs, and presumably the first free‐living cells too. Proton gradients form naturally at alkaline hydrothermal vents and are viewed as central to the origin of life. (...) Here we consider how the earliest cells might have harnessed a geochemically created proton‐motive force and then learned to make their own, a transition that was necessary for their escape from the vents. Synthesis of ATP by chemiosmosis today involves generation of an ion gradient by means of vectorial electron transfer from a donor to an acceptor. We argue that the first donor was hydrogen and the first acceptor CO2. (shrink)

There are two concepts of consciousness that are easy to confuse with one another, access-consciousness and phenomenal consciousness. However, just as the concepts of water and H2O are different concepts of the same thing, so the two concepts of consciousness may come to the same thing in the brain. The focus of this paper is on the problems that arise when these two concepts of consciousness are conflated. I will argue that John Searle’s reasoning about the function of consciousness goes (...) wrong because he conflates the two senses. And Francis Crick and Christof Koch fall afoul of the ambiguity in arguing that visual area V1 is not part of the neural correlate of consciousness. Crick and Koch’s work raises issues that suggest that these two concepts of consciousness may have different (though overlapping) neural correlates--despite Crick and Koch’s implicit rejection of this idea. (shrink)

We have used fMRI to measure responses to chromatic and achromatic contrast in retinotopically defined regions of macaque and human visual cortex. We make four observations. Firstly, the relative amplitudes of responses to color and luminance stimuli in macaque area V1 are similar to those previously observed in human fMRI experiments. Secondly, the dorsal and ventral subdivisions of macaque area V4 respond in a similar way to opponent (L j M)-cone chromatic contrast suggesting that they are part of a single (...) functional area. Thirdly, we find that macaque area V4, like area V1, responds preferentially to chromatic contrast compared to luminance contrast and the degree of preference is strongly influenced by the temporal frequency of the stimulus. Finally, we observe that while macaque V4d is a region on the dorsal surface of the macaque visual cortex that responds robustly to chromatic stimuli, human chromatic responses to identical stimuli are largely confined to the ventral surface suggesting a fundamental difference in the topographical organization of higher visual areas between humans and macaques. (shrink)

Creating focal lesions in primary visual cortex (V1) provides an opportunity to study the role of extra-geniculo-striate pathways for activating extrastriate visual cortex. Previous studies have shown that more than 95% of neurons in macaque area V2 and V3 stop firing after reversibly cooling V1 [1,2,3]. However, no studies on long term recovery in areas V2, V3 following permanent V1 lesions have been reported in the macaque. Here we use macaque fMRI to study area V2, V3 activity patterns from 1 (...) to 22 months after lesioning area V1. We find that visually driven BOLD responses persist inside the V1-lesion projection zones (LPZ) of areas V2 and V3, but are reduced in strength by ,70%, on average, compared to prelesion levels. Monitoring the LPZ activity over time starting one month following the V1 lesion did not reveal systematic changes in BOLD signal amplitude. Surprisingly, the retinotopic organization inside the LPZ of areas V2, V3 remained similar to that of the non-lesioned hemisphere, suggesting that LPZ activation in V2, V3 is not the result of input arising from nearby (non-lesioned) V1 cortex. Electrophysiology recordings of multi-unit activity corroborated the BOLD observations: visually driven multi-unit responses could be elicited inside the V2 LPZ, even when the visual stimulus was entirely contained within the scotoma induced by the V1 lesion. Restricting the stimulus to the intact visual hemi-field produced no significant BOLD modulation inside the V2, V3 LPZs. We conclude that the observed activity patterns are largely mediated by parallel, V1-bypassing, subcortical pathways that can activate areas V2 and V3 in the absence of V1 input. Such pathways may contribute to the behavioral phenomenon of blindsight. (shrink)

The McCollough effect, an orientation-contingent color aftereffect, has been known for over 30 years and, like other aftereffects, has been taken as a means of probing the brain's operations psychophysically. In this paper, we review psychophysical, neuropsychological, and neuroimaging studies of the McCollough effect. Much of the evidence suggests that the McCollough effect depends on neural mechanisms that are located early in the cortical visual pathways, probably in V1. We also review evidence showing that the aftereffect can be induced without (...) conscious perception of the induction patterns. Based on these two lines of evidence, it is argued that our conscious visual experience of the world arises in the cortical visual system beyond V1. (shrink)

In some presentations of classical and intuitionistic logics, the objectlanguage is assumed to contain (two) truth-value constants: ⊤ (verum) and ⊥ (falsum), that are, respectively, true and false under every bivalent valuation. We are interested to define and study analogical constants ‡, 1 ≤ i ≤ n, that in an arbitrary multi-valued logic over truth-values V = {v1,..., vn} have the truth-value vi under every (multi-valued) valuation. As is well known, the absence or presence of such constants has a significant (...) deductive impact on the logics studied. We define such constants proof-theoretically via their associated I/E-rules in a natural-deduction proof system. In particular, we propose a generalization of the notions of contradiction and explosiveness of a logic to the context of multi-valued logics. (shrink)

The RecA family proteins mediate homologous recombination, a ubiquitous mechanism for repairing DNA double‐strand breaks (DSBs) and stalled replication forks. Members of this family include bacterial RecA, archaeal RadA and Rad51, and eukaryotic Rad51 and Dmc1. These proteins bind to single‐stranded DNA at a DSB site to form a presynaptic nucleoprotein filament, align this presynaptic filament with homologous sequences in another double‐stranded DNA segment, promote DNA strand exchange and then dissociate. It was generally accepted that RecA family proteins function throughout (...) their catalytic cycles as right‐handed helical filaments with six protomers per helical turn. However, we recently reported that archaeal RadA proteins can also form an extended right‐handed filament with three monomers per helical turn and a left‐handed protein filament with four monomers per helical turn. Subsequent structural and functional analyses suggest that RecA family protein filaments, similar to the F1‐ATPase rotary motor, perform ATP‐dependent clockwise axial rotation during their catalytic cycles. This new hypothesis has opened a new avenue for understanding the molecular mechanism of RecA family proteins in homologous recombination. BioEssays 30:48–56, 2008. © 2007 Wiley Periodicals, Inc. (shrink)

The ability to initiate DNA replication is a critical step in the proliferation of all organisms. In bacteria, this process is mediated by an ATP‐dependent replication initiator protein, DnaA, which recognizes and melts replication origin (oriC) elements. Despite decades of biochemical and structural work, a mechanistic understanding of how DnaA recognizes and unwinds oriC has remained enigmatic. A recent study by Pelliciari et al. provides important new structural insights into how DnaA from Bacillus subtilis recognizes and processes its cognate oriC, (...) showing how DnaA uses sequence features encoded in the origin to engage melted DNA. Comparison of the DnaA‐oriC structure with archaeal/eukaryl replication origin complexes based on Orc‐family proteins reveals a high degree of similarity in origin engagement by initiators from di domains of life, despite fundamental differences in origin melting mechanisms. These findings provide valuable insights into bacterial replication initiation and highlight the intriguing evolutionary history of this fundamental biological process. (shrink)

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V1) andA(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the (...) vacuum state between events inA(V1) andA(V2) have a genuinely probabilistic common cause, then the local algebrasA(V1) andA(V2) must be statistically independent in the sense of C*-independence. (shrink)

How tight is the conceptual connection between imagination and perception? A number of philosophers, from the early moderns to present-day predictive processing theorists, tie the knot as tightly as they can, claiming that states of the imagination, i.e. mental imagery, are a proper subset of perceptual experience. This paper labels such a view ‘perceptualism’ about the imagination and supplies new arguments against it. The arguments are based on high-level perceptual content and, distinctly, cognitive penetration. The paper also defuses a recent, (...) influential argument for perceptualism based on the ‘discovery’ that visual perception and mental imagery share a significant neural substrate: circuitry in V1, the brain’s primary visual cortex. Current neuropsychology is shown to be equivocal at best on this matter. While experiments conducted on healthy, neurotypical subjects indicate substantial neural overlap, there is extensive clinical evidence of dissociations between imagery and perception in the brain, most notably in the case of aphantasia. (shrink)

Kohlenbach, U., Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation, Annals of Pure and Applied Logic 64 27–94.We consider uniqueness theorems in classical analysis having the form u ε U, v1, v2 ε Vu = 0 = G→v 1 = v2), where U, V are complete separable metric spaces, Vu is compact in V and G:U x V → is a constructive function.If is proved by arithmetical means from analytical assumptions x (...) εXy ε Yx z ε Z = 0) only , then we can extract from the proof of → an effective modulus of uniqueness, which depends on u, k but not on v1,v2, i.e., u ε U, v1, v2 ε Vu, k εG, G 2-φuk→dv2-itk). Such a modulus φ can e.g. be used to give a finite algorithm which computes the zero of G on Vu with prescribed precision if it exists classically.The extraction of φ uses a proof-theoretic combination of functional interpretation and pointwise majorization. If the proof of → uses only simple instances of induction, then φ is a simple mathematical operation. (shrink)

Introduction There are some exceptions, which we shall see below, but virtually all theories in psychology and cognitive science make use of the notion of representation. Arguably, folk psychology also traffics in representations, or is at least strongly suggestive of their existence. There are many different types of things discussed in the psychological and philosophical literature that are candidates for representation-hood. First, there are the propositional attitudes – beliefs, judgments, desires, hopes etc. (see Chapters 9 and 17 of this volume). (...) If the propositional attitudes are representations, they are person-level representations – the judgment that the sun is bright pertains to John, not a subpersonal part of John. By contrast, the representations of edges in V1 of the cerebral cortex that neuroscientists talk about and David Marr’s symbolic representations of “zero-crossings” in early vision (Marr 1982) are at the “sub-personal” level – they apply to parts or states of a person (e.g. neural parts or computational states of the visual system). Another important distinction is often made among perceptual, cognitive, and action-oriented representations (e.g. motor commands). Another contrast lies between “stored representations” (e.g. memories) and “active representations” (e.g. a current perceptual state). Related to this is the distinction between “dispositional representations” and “occurrent representations.” Beliefs that are not currently being entertained are dispositional, e.g. your belief that the United States is in North America - no doubt you had this belief two minutes ago, but you were not consciously accessing it until you read this sentence. Occurrent representations, by contrast, are active, conscious thoughts or perceptions. Which leads us to another important distinction: 1 between conscious and non-conscious mental representations, once a bizarre-sounding distinction that has become familiar since Freud (see Chapter 4 of this volume). I mention these distinctions at the outset to give you some idea of the range of phenomena we will be considering, and to set the stage for our central “problem of representation”: what is a mental representation, exactly, and how do we go about deciding whether there are any? We know there are public representations of various kinds: words, maps, and pictures, among others.. (shrink)