Let p ≥ 5 be a prime and k be an integer in [ 2 p + 2 , p 2 - p + 3 ] . Let b be in [ 2 , p ] such that k - 2 ≡ b mod p - 1 and c : = k - 2 - b p - 1 . We give an explicit radius of local constancy in the weight space of the mod p reduction of the two dimensional crystalline representations V k , a p of Gal ( ℚ ¯ p / ℚ p ) , where the slope ν ( a p ) is constrained to be in ( 1 , c ) and non-integral. We use the mod p local Langlands correspondence for GL 2 ( ℚ p ) to compute the mod p reductions explicitly under additional conditions on the slope. We show that the reduction in the disk depends only on k and ⌊ ν ( a p ) ⌋ . As an application, we obtain explicit mod p reductions at many new values of k and a p . We also obtain an explicit radius of local constancy in the a p space (for a fixed k as above) which is bigger than the explicit radius given in a result of Berger.

Can we maintain space constancy in virtual environments?

This article presents a qualitative and quantitative study of personality based on psychosemantic technique “color-associative experiment”. The subject of this research is the theoretical framework, procedure for psychosemantic technique “color-associative experiment”, and the possibilities of its application in psychological counseling of students. For quality data processing and interpretation, the author employs the techniques of free and axial coding (the categories correspond to the axes: conditions, phenomenon, its characteristics, strategy of interaction with the phenomenon, and outcome), which allow the psychologist to acquire a holistic representation on the current state of the respondent. The article provides the materials of empirical study, which involved 15 people; describes the results diagnostics of the bachelor's degree students conducted in terms of distance learning at the Academy for the Humanities and Pedagogy  (branch) of the Crimean Federal University in Yalta (April 2020). The obtained results indicate that the verbal space and perceptive-semantic space are not identical, but mutually complementary, forming a holistic picture of the individual semantic space of personality. On the example of implementation of “color-associative experiment” technique, the respondent (bachelor's degree graduate) is characterized by a neurotic structure of personality. The intrapersonal conflict and resulting emotional tension are accompanied by the pursuit of orderliness and freedom (the verbal component of semantic space), but also indicate the prevalence of variability and lack of constancy in the perceptive semantic space of personality. For comparing the results of perceptive and verbal semantic space, the author offers the schematic image of the coordinate system formed by these two axes and saturated with individual meanings of the respondent. Thus, in the dialogue with the respondent, the psychologist forms a map of the individual semantic space of the latter. The application of the method of “color-associative experiment” indicated the instance of the development of reflection among students.

To achieve visual space constancy, our brain remaps eye-centered projections of visual objects across saccades. Here, we measured saccade trajectory curvature following the presentation of visual, auditory, and audiovisual distractors in a double-step saccade task to investigate if this stability mechanism also accounts for localized sounds. We found that saccade trajectories systematically curved away from the position at which either a light or a sound was presented, suggesting that both modalities are represented in eye-centered oculomotor centers. Importantly, the same effect was observed when the distractor preceded the execution of the first saccade. These results suggest that oculomotor centers keep track of visual, auditory and audiovisual objects by remapping their eye-centered representations across saccades. Furthermore, they argue for the existence of a supra-modal map which keeps track of multi-sensory object locations across our movements to create an impression of space constancy.

We study the mod $p$ reduction of crystalline local Galois representations of dimension 2 under certain conditions on its weight and slope. Berger showed that for a fixed non-zero trace of the Frobenius, the reduction process is locally constant for varying weights. By explicit computation we obtain an upper bound that is a linear function of the slope, for the radius of this local constancy around some special points in the weight space.

We study some qualitative properties of ancient solutions of superlinear heat equations on a Riemannian manifold, with particular interest in positivity and constancy in space.

Bridgemanian space constancy as a precursor to extended cognition.

This paper reports the benefits of combined integrated learning programme (CILP) in the early rehabilitation of learning disability child. Learning disability is coined by Samuel kirk in 1963 to describe children who have significant difficulties in understanding various language, reading, writing and other mathematical problems. An intervention of 60 days (6 days per week for 10 weeks) was given to the child and prognosis was observed on various outcome variables like Eye hand coordination (EHC), Figure ground perception (FGP), Figure constancy (FC) and Position in space (PIS) before and after the interventions. Considerable improvement was seen by applying CiLP programme in child with learning disability.

The perceived size of an object remains relatively constant although its retinal size keeps decreasing as the object moves away along the depth dimension of the 3D space, i.e. size constancy. Neural mechanisms generating size constancy in virtual 3D space, however, remain poorly understood. By constructing a virtual 3D world in the MR scanner, we positioned the same 3D objects either near or far from the observers so that the near and far objects were perceived as having the same physical size despite their differences in retinal size. To control for the effect of differential retinal size, an additional 2D condition was introduced: a large and a small object, with matched retinal images as the near and far objects in the 3D condition, respectively, were presented on a 2D screen. Differences in retinal size activated overlapped areas in bilateral inferior occipital gyrus (IOG) in both experiments. The overlapped areas in IOG, however, showed different patterns of functional connectivity with different neural networks, depending on the perceived size of objects. In particular, IOG showed enhanced connectivity with bilateral superior parietal cortex in the 2D condition, but with inferior temporal and prefrontal cortex in the virtual 3D condition, i.e., size constancy.

We study the qualitative properties of ancient solutions of linear and semilinear heat equations in a Riemannian manifold, with particular attention to positivity and constancy in space.

It has been shown with using a complex 3-D configuration of reference points, that, in the presence of rich afterimage (rA), eye movements lead to transformation of the visual field, representing a complex rotation and scale transformation of 3-D space with a center somewhere in the region of a hypothetical "cyclopean eye". Experiments have shown that this also results in the recalculation of the coordinates of the observer's gaze direction, entirely based on inflow information, independent on the signals of the oculomotor efferent system. Three types of rA illusions are described under different kinds of eye movements. A model is again (after 1976) expressed that these phenomena reflect the work of the "contextually" independent Screen Constancy Mechanisms (SCM), which operate at the hypothetical Constant Visual Screen (CVS) level. This level can still be considered as "pseudo-sensory" one of the visual system, located before the formation (appearance) of the object-structured visual field. In experiments, certain conditions affecting the degree of afterimage "richness have been also investigated.

Although action and perception are different behaviors, they are likely to be interrelated, as implied by the notions of perception-action coupling and active sensing. Traditionally, it has been assumed that the nervous system directly preprograms motor commands required for actions and uses a copy of them called efference copy (EC) to also influence our senses. This review offers a critical analysis of the EC concept by identifying its limitations. An alternative to the EC concept is based on the experimentally confirmed notion that sensory signals from receptors are perceived relative to referent signals specified by the brain. These referents also underlie the control of motor actions by predetermining where, in the spatial domain, muscles can work without preprogramming how they should work in terms of motor commands or EC. This approach helps solve several problems of action and explain several sensory experiences, including position sense and the sense that the world remains stationary despite changes in its retinal image during eye or body motion (visual space constancy). The phantom limb phenomenon and other kinesthetic illusions are also explained within this framework.

The relationship between large-scale gradients in species richness and functional diversity provides important information regarding the mechanisms driving patterns of biodiversity. A classic hypothesis in ecology is that strong interspecific interactions should result in an increase in the functional volume of assemblages as the species richness increases, whereas climatic constraints may result in no change in functional volume. Most research of this kind examines latitudinal gradients in species richness, but the results are likely confounded by underlying gradients in climate and phylogenetic composition. We take an alternative approach that examines functional richness across a tree species richness anomaly where species richness doubles from Europe to eastern North America. The results demonstrate that the functional richness on both continents saturates at a similar point as species richness increases and that the packing of functional space becomes tighter. Further, the species richness anomaly is driven primarily by genera unique to North America, but those genera contribute less than expected functional richness to the region, indicating a high level of redundancy with genera shared between the continents. Taken together, the results indicate that the species richness anomaly is associated with diversification within a climatically constrained trait space. More generally, the work demonstrates the power of utilizing species richness anomalies in biodiversity research, particularly when they are coupled with information regarding organismal function.

Constancy of local spread rates for buffelgrass (Pennisetum ciliare L.) in the Arizona Upland of the Sonoran Desert

Different attention and saccade control areas contribute to space constancy by remapping target activity onto their expected post-saccadic locations. To visualize this dynamic remapping, we used a technique developed by Honda (2006) where a probe moved vertically while participants made a saccade across the motion path. Observers do not report any large excursions of the trace at the time of the saccade that would correspond to the classical peri-saccadic mislocalization effect. Instead, they reported that the motion trace appeared to be broken into two separate segments with a shift of approximately one-fifth of the saccade amplitude representing an overcompensation of the expected retinal displacement caused by the saccade. To measure the timing of this break in the trace, we introduced a second, physical shift that was the same size but opposite in direction to the saccade-induced shift. The trace appeared continuous most frequently when the physical shift was introduced at the midpoint of the saccade, suggesting that the compensation is in place when the saccade lands. Moreover, this simple linear shift made the combined traces appear continuous and linear, with no curvature. In contrast, Honda (2006) had reported that the pre- and post-saccadic portion of the trace appeared aligned and that there was often a small, visible excursion of the trace at the time of the saccade. To compare our results more directly, we increased the contrast of our moving probe in a third experiment. Now some observers reported seeing a deviation in the motion path but the misalignment remained present. We conclude that the large deviations at the time of saccade are generally masked for a continuously moving target but that there is nevertheless a residual misalignment between pre- and post-saccadic coordinates of approximately 20% of the saccade amplitude that normally goes unnoticed.

The transpolar drift is strongly enriched in 228Ra accumulated on the wide Arctic shelves with subsequent rapid offshore transport. We present new data of Polarstern expeditions to the central Arctic and to the Kara and Laptev seas. Because 226Ra activities in Pacific waters are 30% higher than in Atlantic waters, we correct 226Ra for the Pacific admixture when normalizing 228Ra with 226Ra. The use of 228Ra decay as age marker critically depends on the constancy in space and time of the source activity, a condition that has not yet adequately been tested. While 228Ra decays during transit over the central basin, ingrowth of 228Th could provide an alternative age marker. The high 228Th/228Ra activity ratio (AR = 0.8–1.0) in the central basins is incompatible with a mixing model based on horizontal eddy diffusion. An advective model predicts that 228Th grows to an equilibrium AR, the value of which depends on the scavenging regime. The low AR over the Lomonosov Ridge (AR = 0.5) can be due to either rapid transport (minimum age without scavenging 1.1 year) or enhanced scavenging. Suspended particulate matter load (derived from beam transmission and particulate 234Th) and total 234Th depletion data show that scavenging, although extremely low in the central Arctic, is enhanced over the Lomonosov Ridge, making an age of 3 years more likely. The combined data of 228Ra decay and 228Th ingrowth confirm the existence of a recirculating gyre in the surface water of the eastern Eurasian Basin with a river water residence time of at least 3 years.

While participants made 10° horizontal saccades, two dots were presented, one before and one after the saccade. Each dot was presented for 400 ms, the first turned off about 100 ms before, while the second turned on about 100 ms after the saccade. The two dots were separated vertically by 3°, but because of the intervening eye movement, they were also separated horizontally on the retina by an additional 10°. Participants nevertheless reported that the perceived motion was much more vertical than horizontal, suggesting that the trans-saccadic displacement was corrected, at least to some extent, for the retinal displacement caused by the eye movement. The corrections were not exact, however, showing significant biases that corresponded to about 5% of the saccade amplitude. The perceived motion between the probes was tested at 9 different locations and the biases, the deviations from accurate correction, varied significantly across locations. Two control experiments for judgments of position and of verticality of motion without eye movement confirmed that these biases are specific to the correction for the saccade. The local variations in the correction for saccades are consistent with physiological "remapping" proposals for space constancy that individually correct only a few attended targets but are not consistent with global mechanisms that predict the same correction at all locations.

Pharmacological treatment of children with ADHD has been shown to be successful; however, medication may not normalize attention functions. The present study was based on a neuropsychological model of attention and assessed the effect of an attention training program on attentional functioning of children with ADHD. Thirty-two children with ADHD and 16 healthy children participated in the study. Children with ADHD were randomly assigned to one of the two conditions, i.e., an attention training program which trained aspects of vigilance, selective attention and divided attention, or a visual perception training which trained perceptual skills, such as perception of figure and ground, form constancy and position in space. The training programs were applied in individual sessions, twice a week, for a period of four consecutive weeks. Healthy children did not receive any training. Alertness, vigilance, selective attention, divided attention, and flexibility were examined prior to and following the interventions. Children with ADHD were assessed and trained while on ADHD medications. Data analysis revealed that the attention training used in the present study led to significant improvements of various aspects of attention, including vigilance, divided attention, and flexibility, while the visual perception training had no specific effects. The findings indicate that attention training programs have the potential to facilitate attentional functioning in children with ADHD treated with ADHD drugs.

Space constancy, the appearance of a stable visual world despite shifts of all visual input with each eye movement, has been explained historically with a compensatory signal (efference copy or corollary discharge) that subtracts the eye movement signal from the retinal image shift accompanying each eye movement. Quantitative measures have shown the signal to be too small and too slow to mediate space constancy unaided. Newer theories discard the compensation idea, instead calibrating vision to each saccadic target.

The present study is concerned with the problem of compensation for smooth pursuit eye movements, especially with the timing of this compensation. When the eyes are engaged in a pursuit movement, a stationary background moves on the retina on the opposite direction. The visual system compensates for this retinocentric motion, recovering the stability of the visual environment. The compensation is incomplete, giving rise to the Filehne illusion, in which a stationary background is perceived as moving slightly in the direction opposite to the pursuit. How long does it take to the visual system to compensate for those eye movements? Although this issue has received some attention in psychophysics (Stoper, 1967, Mack and Herman, 1978) and in neurophysiology (Haarmeier and Thier, 1998, Hoffmann and Bach, 2002, Tikhonov et al., 2004), little evidence of time evolution of compensation has been presented. Recently, we have introduced a new technique to study the time evolution of compensation in the case of motion detection (VSS 2004). We found that in as little as 150 ms following stimulus appearance, motion is detected with respect to an allocentric reference frame; earlier, only motion in a retinocentric frame is detected. Thus, in the case of motion detection, compensation is in place by 150 ms. Here, we ask whether the time evolution of compensation is specific to motion detection or whether it generalizes to other visual tasks. In the first experiment, we measured the time course of the Filehne illusion for extremely brief durations. In the second experiment, we study whether manually displacing the pursuit target—which reduces the time lag between target and eye movements—has an effect on the time course of compensation.