On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

A calculus for the common rules of ∧ and ∨

We provide a finite axiomatization of the consequence , i.e. of the set of common sequential rules for and . Moreover, we show that has no proper non-trivial strengthenings other than and . A similar result is true for , but not, e.g., for ⁺.To the memory of Jerzy Supecki     

A note on syntactical and semantical functions

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class ^–1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).     

The Deep Structure of Group Life: Unconscious Dimensions

There is a reconsideration and renaissance of interest in expanded conceptions of unconscious processes as they affect individuals and groups (Grotstein, 1999). Recent focus on social unconscious (Hopper, 1996) and cultural unconscious processes (Henderson, 1988) and the nature of intersubjectivity (Harwood and Pines, 1998) raise questions about the location of group analysis. This paper considers the deep structure of group life by examining four functions of the unconscious: repressive, conservative, creative, and mythopoetic (Ellenberger, 1970). On an individual level of analysis, these functions are equated respectively with formative ideas about the: personal–subjective, social–political, intersubjective–cultural and collective–objective unconscious. Group level analogs, as they develop and affect groups and their members, are explored as synthetic, shared, symbolicy and synchronous unconscious processes.     

Saving the Truth Schema from Paradox

The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr(A)A (understood as the conjunction of Tr(A)A and ATr(A)). We also keep the full intersubstitutivity of Tr(A)) with A in all contexts, even inside of an . Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the ; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary.     

A brief nap is beneficial for human route-learning: The role of navigation experience and EEG spectral power

Here, we examined the effect of a daytime nap on changes in virtual maze performance across a single day. Participants either took a short nap or remained awake following training on a virtual maze task. Post-training sleep provided a clear performance benefit at later retest, but only for those participants with prior experience navigating in a three-dimensional (3D) environment. Performance improvements in experienced players were correlated with delta-rich stage 2 sleep. Complementing observations that learning-related brain activity is reiterated during post-navigation NREM sleep in rodents, the present data demonstrate that NREM sleep confers a performance advantage for spatial memory in humans.A growing body of animal and human literature suggests that the consolidation of memories occurs optimally during periods of post-learning sleep. Nonrapid eye movement sleep (NREM), in particular, may be beneficial for the offline consolidation of hippocampus-dependent learning. The neurophysiological basis for this hypothesis is derived largely from electrophysiological studies in rodents, demonstrating that patterns of hippocampal place cell activity first seen during waking exploration are later reexpressed during post-learning sleep (Wilson and McNaughton 1994; Kudrimoti et al. 1999; Nadasdy et al. 1999; Ji and Wilson 2007). Behavioral studies in humans meanwhile demonstrate that NREM sleep is beneficial for declarative memory performance, relative to equivalent periods of wakefulness (Plihal and Born 1997; Tucker et al. 2006). However, the memory tasks typically employed in human research are quite different from those used in rodents, with human studies most often focusing on the memorization of verbal or visual stimuli (Plihal and Born 1997; Schabus et al. 2004; Clemens et al. 2005; Ellenbogen et al. 2006; Tucker et al. 2006; Daurat et al. 2008). Thus far, sleep-dependent memory reactivation has not been established to be directly beneficial for memory performance in an animal model, as the protocols employed in this research typically involve well-learned simple tasks which do not easily lend themselves to measurement of learning across time (Wilson and McNaughton 1994; Kudrimoti et al. 1999). Although the hippocampal memory reactivation described in rodents is a possible explanation for the effect of NREM sleep on human declarative memory, widely divergent methodologies employed across species prohibit confidence in this conclusion.Bridging this conceptual gap, a small handful of studies have begun to explore the relationship between spatial navigation and NREM sleep in humans. Notably, a PET study by Peigneux et al. (2004) demonstrated that learning-related hippocampal activity seen while training on a virtual maze task is again expressed during post-learning human sleep. Furthermore, this hippocampal reactivation strongly predicted overnight improvement on the task (Peigneux et al. 2004). Additional studies have suggested a link between sleep and other types of spatial-related learning, including mental rotation performance (Plihal and Born 1999), the ability to reproduce a complex figure (Clemens et al. 2006; Tucker and Fishbein 2008), performance on a computerized version of Milner''s (1965) “bolt head” maze (Tucker and Fishbein 2008), and memory for the location of verbal information on a screen (Daurat et al. 2008).Yet it remains unclear whether sleep, relative to wakefulness, provides a performance benefit for human route-learning in the context of a realistic spatial environment. Navigation through virtual environments is a strongly hippocampus-dependent task (Peigneux et al. 2004; Astur et al. 2005) and provides an experimental model closely paralleling the spatial exploration tasks employed in the rodent literature. However, the few studies reporting effects of sleep on human navigation performance have been contradictory. Using a navigation task similar to that of Peingeux et al. (2004), Orban et al. (2006) failed to detect any effect of post-learning sleep deprivation on maze performance but did find evidence of altered task-related brain activity, concluding that sleep supports “covert” memory reorganization (Orban et al. 2006). In direct contrast, Ferrara et al. found that spatial memory is improved when a retention interval falls across a night of sleep, relative to when route memory must be retained during daytime wakefulness, or across a night of sleep deprivation (Ferrara et al. 2006, 2008).The present study clarifies these issues by examining the effect of a post-learning nap on complex route-learning in a three-dimensional (3D) virtual environment. When controls are tested at a different time of day than sleep participants, circadian confounds may present a substantial problem. Alternatively, overnight protocols employing sleep-deprived subjects necessarily suffer from confounds related to this sleep deprivation during the retention interval. The use of a daytime nap as a sleep intervention avoids these pitfalls by allowing all subjects to be trained and tested at the same circadian time, and in the absence of sleep deprivation. A series of recent studies confirm that a daytime nap is sufficient to induce performance improvements on declarative and procedural memory tasks, relative to wake subjects (Mednick et al. 2003; Backhaus and Junghanns 2006; Nishida and Walker 2006; Tucker et al. 2006; Lahl et al. 2008; Tucker and Fishbein 2008).Participants (n = 53, 34 female) were trained on a virtual maze-learning task at 12:30 pm. Following training, nap participants lay down for a 1.5-h sleep opportunity. These subjects were allowed to obtain as much NREM sleep as possible but were awoken at the first signs of REM (see Table 

The American plan completed: Alternative classical-style semantics,without stars,for relevant and paraconsistent logics

American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 (A, a) iff 0 (A, a) and 0 (A, a) iff 1 (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The cost of these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa.     

Improving Identity Matching of Newly Encountered Faces: Effects of Multi-image Training

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Behavioral deficits and subregion-specific suppression of LTP in mice expressing a population of mutant NMDA receptors throughout the hippocampus

The NMDA receptor (NMDAR) subunit GluN1 is an obligatory component of NMDARs without a known functional homolog and is expressed in almost every neuronal cell type. The NMDAR system is a coincidence detector with critical roles in spatial learning and synaptic plasticity. Its coincidence detection property is crucial for the induction of hippocampal long-term potentiation (LTP). We have generated a mutant mouse model expressing a hypomorph of the Grin1^N598R allele, which leads to a minority (about 10%) of coincidence detection-impaired NMDARs. Surprisingly, these animals revealed specific functional changes in the dentate gyrus (DG) of the hippocampal formation. Early LTP was expressed normally in area CA1 in vivo, but was completely suppressed at perforant path-granule cell synapses in the DG. In addition, there was a pronounced reduction in the amplitude of the evoked population spike in the DG. These specific changes were accompanied by behavioral impairments in spatial recognition, spatial learning, reversal learning, and retention. Our data show that minor changes in GluN1-dependent NMDAR physiology can cause dramatic consequences in synaptic signaling in a subregion-specific fashion despite the nonredundant nature of the GluN1 gene and its global expression.According to Hebb''s postulate, neurons require a molecular mechanism to detect synchronous activity in order to change the strength of synaptic connectivity (Hebb 1949). NMDA receptors (NMDARs) are molecular coincidence detectors, and selective NMDAR antagonists block the induction of long-term potentiation (LTP) in both the dentate gyrus (DG) and CA1 regions of the hippocampus (Bliss and Collingridge 1993; Martin et al. 2000). NMDARs have been long known for their role in spatial learning, but more recently have been implicated in other forms of cognitive function and dysfunction (Gruart et al. 2006; Whitlock et al. 2006; Castner and Williams 2007; Kristiansen et al. 2007; Wilson and Linster 2008).Neuronal NMDARs are hetero-tetrameric ligand-gated ion channels typically comprised of two types of subunits. Two copies of the mandatory GluN1 subunit (or NR1 subunit [Collingridge et al. 2009] encoded by Grin1) are associated with two copies from the GluN2 family, GluN2A–D (or NR2A–D). The GluN1 subunit is expressed ubiquitously both spatially and temporally throughout the developing and adult brain. Global knockout mice models of the GluN1 subunit are postnatally lethal within hours after birth (Forrest et al. 1994; Li et al. 1994), and cell-specific GluN1 mice knockouts (Tsien et al. 1996; Nakazawa et al. 2002; McHugh et al. 2007; Niewoehner et al. 2007) have provided insights on how specific synapses and regional neuronal networks are dependent on NMDAR function.The early postnatal lethality of the global GluN1 knockout is in contrast to the null mutants of the four AMPA receptor genes and other major synaptic proteins, such as αCaMKII (Silva et al. 1992a,b; Jia et al. 1996; Zamanillo et al. 1999; Meng et al. 2003). This can be at least partially explained by the absence of any close GluN1 homologs, which could functionally compensate for the absence of the GluN1 subunit. Recombinant expression studies defined the GluN1 subunit as a mandatory component of NMDARs. This constellation provides a specific opportunity to test whether different local neuronal subnetworks are affected differentially by mutant Grin1 alleles associated with subtle alterations of the functional properties of NMDARs.GluN1 subunits with the N598R point mutation (GluN1^R) yield functional NMDARs that are Mg²⁺ insensitive and Ca²⁺ impermeable (Burnashev et al. 1992; Mori et al. 1992). The Grin1^N598R allele that codes for GluN1^R subunits is a gain-of-function mutation that is dominant lethal, even in heterozygous and hemizygous lines (Single et al. 2000; Rudhard et al. 2003). NMDARs with GluN1^R subunits do not act as coincidence detectors and, interestingly, mice expressing exclusively the GluN1^R allele lack whisker-related pattern formation in the neonate brainstem (Rudhard et al. 2003).To investigate the functional importance of GluN1 subunits with the N598R point mutation, we took advantage of the generation of a variant mutant line of mice (GluN1^Rneo/+) expressing a minority (around 10%) of these mutant NMDARs. Even though the majority of the NMDARs are normal, all neurons expressing NMDARs will contain a subset of receptors carrying this mutation.Therefore, this mouse model is an ideal candidate to study the impact of subtle alterations of NMDAR function on different neuronal networks, such as those comprising the hippocampal formation.Studies examining region-specific targeted disruption of GluN1 expression in subregions of the hippocampus have revealed subtle yet important contributions of this NMDAR subunit in synaptic plasticity and spatial learning and memory. CA1-restricted knockout of GluN1 expression in the hippocampus caused impaired spatial learning and memory as well as reduced CA1-LTP (Tsien et al. 1996). In the case of the disruption of GluN1 expression in the DG region of the hippocampus, more subtle behavioral impairments were apparent, including the inability to discriminate between two similar contexts (pattern separation) and deficits in spatial working memory despite normal LTP in the CA1 region (McHugh et al. 2007; Niewoehner et al. 2007).Our GluN1^Rneo/+ mice differ from the region-specific GluN1 mutant mice in that they express the mutant hypomorph at the same level in different subregions of the hippocampus. Interestingly, we found that this allele leads to substantial differences in short- and long-term plasticity between area CA1 and the DG of the hippocampus. The specific impairment in the DG was accompanied by impaired spatial recognition, spatial learning, reversal learning, and retention. Our data establish the possibility of a circuit-specific phenotype caused by a mutant variant of a globally expressed major nonredundant synaptic protein.     

Interactions between prefrontal cortex and cerebellum revealed by trace eyelid conditioning

Eyelid conditioning has proven useful for analysis of learning and computation in the cerebellum. Two variants, delay and trace conditioning, differ only by the relative timing of the training stimuli. Despite the subtlety of this difference, trace eyelid conditioning is prevented by lesions of the cerebellum, hippocampus, or medial prefrontal cortex (mPFC), whereas delay eyelid conditioning is prevented by cerebellar lesions and is largely unaffected by forebrain lesions. Here we test whether these lesion results can be explained by two assertions: (1) Cerebellar learning requires temporal overlap between the mossy fiber inputs activated by the tone conditioned stimulus (CS) and the climbing fiber inputs activated by the reinforcing unconditioned stimulus (US), and therefore (2) trace conditioning requires activity that outlasts the presentation of the CS in a subset of mossy fibers separate from those activated directly by the CS. By use of electrical stimulation of mossy fibers as a CS, we show that cerebellar learning during trace eyelid conditioning requires an input that persists during the stimulus-free trace interval. By use of reversible inactivation experiments, we provide evidence that this input arises from the mPFC and arrives at the cerebellum via a previously unidentified site in the pontine nuclei. In light of previous PFC recordings in various species, we suggest that trace eyelid conditioning involves an interaction between the persistent activity of delay cells in mPFC-a putative mechanism of working memory-and motor learning in the cerebellum.Eyelid conditioning is a form of associative learning that has proven useful for mechanistic studies of learning (Thompson 1986). All variants of eyelid conditioning involve pairing a conditioned stimulus (CS, typically a tone) with a reinforcing unconditioned stimulus (US, mild electrical stimulation near the eye) to promote learned eyelid closure in response to the CS (also known as a conditioned response). Delay eyelid conditioning, where the CS and US overlap in time (Fig. 1A , left), is largely unaffected by forebrain lesions (Solomon et al. 1986; Mauk and Thompson 1987; Kronforst-Collins and Disterhoft 1998; Weible et al. 2000; Powell et al. 2001; McLaughlin et al. 2002) and engages the cerebellum relatively directly (but see Halverson and Freeman 2006). Presentation of the tone and the US are conveyed to the cerebellum via activation of mossy fibers and climbing fibers, respectively (Fig. 1B; Mauk et al. 1986; Steinmetz et al. 1987, 1989; Sears and Steinmetz 1991; Hesslow 1994; Hesslow et al. 1999). In addition, output via a cerebellar deep nucleus is required for the expression of conditioned responses (McCormick and Thompson 1984). This relatively direct mapping of stimuli onto inputs and of output onto behavior makes delay eyelid conditioning a powerful tool for the analysis of cerebellar learning and computation (Mauk and Donegan 1997; Medina and Mauk 2000; Medina et al. 2000, 2002; Hansel et al. 2001; Ohyama et al. 2003).Open in a separate windowFigure 1.The procedures, neural pathways, and putative signals involved in delay and trace eyelid conditioning. (A) Stimulus timing for delay (left) and trace (right) training trials. For delay conditioning, the US overlaps in time with the tone CS. In this and subsequent figures, green is used to indicate the presentation of the CS for delay conditioning. For trace conditioning, the US is presented after CS offset, and “trace interval” refers to the period between CS offset and US onset. For convenience, we used red and maroon regions to represent the CS and trace interval, respectively. Sample conditioned eyelid responses are shown below, for which an upward deflection indicates closure of the eyelid. (B) Schematic representation of the pathways engaged by delay conditioning. The CS and US, respectively, engage mossy fibers and climbing fibers relatively directly, and forebrain input is not required for normal learning. (C) The signals hypothesized to engage the cerebellum during trace conditioning. The activity of mossy fibers directly activated by the tone CS does not significantly outlast the stimulus. Thus, a forebrain structure is thought to provide an input that overlaps in time with the US and is necessary to produce cerebellar learning.Trace eyelid conditioning, where the US is presented after tone offset (Fig. 1A, right), has attracted interest for its potential to reveal the nature of interactions between the forebrain and cerebellum as well as the learning mechanisms within these systems. This potential stems from the sensitivity of trace conditioning not only to lesions of cerebellum but also to lesions of hippocampus, medial prefrontal cortex (mPFC), or mediodorsal thalamic nucleus (Woodruff-Pak et al. 1985; Moyer Jr. et al. 1990; Kronforst-Collins and Disterhoft 1998; Weible et al. 2000; Powell et al. 2001; McLaughlin et al. 2002; Powell and Churchwell 2002; Simon et al. 2005). Given the general inability of forebrain lesions to affect delay conditioning, these results have promoted the general interpretation that the forebrain and cerebellum interact to mediate trace conditioning (Weiss and Disterhoft 1996; Clark and Squire 1998; Clark et al. 2002).Here we test the specific hypotheses that (Fig. 1C) (1) cerebellar learning requires that mossy fiber and climbing fiber inputs overlap in time (or nearly so) and (2) that cerebellar learning in trace conditioning occurs in response to a forebrain-driven mossy fiber input that outlasts the CS to overlap with the US rather than the inputs activated by the tone CS (Clark et al. 2002). The data provide direct support for both assertions and, together with recent anatomical studies (Buchanan et al. 1994; Weible et al. 2007), reveal a pathway between the mPFC and cerebellum that is necessary for the expression of trace eyelid responses. When combined with previous recordings from PFC in primates and rodents (Funahashi et al. 1989; Bodner et al. 1996; Fuster et al. 2000; Narayanan and Laubach 2006), these data support the hypothesis that trace eyelid conditioning is mediated by interactions between working memory-related persistent activity in mPFC and motor learning mechanisms in the cerebellum.     

Hybrids of the -translation for

In [W. Burr, Functional interpretation of Aczel's constructive set theory, Annals of Pure and Applied Logic 104 (2000) 31–73] Wolfgang Burr presents a functional interpretation of constructive set theory in all finite types, , in a theory of constructive set functionals. is a subtheory of , containing bounded quantifiers only. His interpretation theorem reduces the consistency problem of (and certain extensions thereof) to the consistency problem of .We want to study admissible rules in , i.e. rules under which is closed. To do so, we study a Troelstra-style q-hybrid of, in fact, a modification ^× of Burr's translation. We introduce this modification in order to close a minor gap in Burr's proof of the functional interpretation of the schema of (Strong Collection).First of all, but surely after a short introduction, we analyse the less complex translation of modified realisation ^mr and its hybrids ^mq and ^mrt.