Renormalization and resummation in the O(N) model

In the O(N) model for the large N expansion one needs resummation which makes the renormalization of the model difficult. In the paper it is discussed, how can one perform a consistent perturbation theory at zero as well as at finite temperature with the help of momentum dependent renormalization schemes.Comment: 4 pages, presented at International Conference on Strong and Electroweak matter (SEWM 2008), Amsterdam, The Netherlands, 26-29 Aug 200

Encoding of Intention and Spatial Location in the Posterior Parietal Cortex

The posterior parietal cortex is functionally situated between sensory cortex and motor cortex. The responses of cells in this area are difficult to classify as strictly sensory or motor, since many have both sensory- and movement-related activities, as well as activities related to higher cognitive functions such as attention and intention. In this review we will provide evidence that the posterior parietal cortex is an interface between sensory and motor structures and performs various functions important for sensory-motor integration. The review will focus on two specific sensory-motor tasks-the formation of motor plans and the abstract representation of space. Cells in the lateral intraparietal area, a subdivision of the parietal cortex, have activity related to eye movements the animal intends to make. This finding represents the lowest stage in the sensory-motor cortical pathway in which activity related to intention has been found and may represent the cortical stage in which sensory signals go "over the hump" to become intentions and plans to make movements. The second part of the review will discuss the representation of space in the posterior parietal cortex. Encoding spatial locations is an essential step in sensory-motor transformations. Since movements are made to locations in space, these locations should be coded invariant of eye and head position or the sensory modality signaling the target for a movement Data will be reviewed demonstrating that there exists in the posterior parietal cortex an abstract representation of space that is constructed from the integration of visual, auditory, vestibular, eye position, and propriocaptive head position signals. This representation is in the form of a population code and the above signals are not combined in a haphazard fashion. Rather, they are brought together using a specific operation to form "planar gain fields" that are the common foundation of the population code for the neural construct of space

Visual and eye movement functions of the posterior parietal cortex

Lesions of the posterior parietal area in humans produce interesting spatial-perceptual and spatial-behavioral deficits. Among the more important deficits observed are loss of spatial memories, problems representing spatial relations in models or drawings, disturbances in the spatial distribution of attention, and the inability to localize visual targets. Posterior parietal lesions in nonhuman primates also produce visual spatial deficits not unlike those found in humans. Mountcastle and his colleagues were the first to explore this area, using single cell recording techniques in behaving monkeys over 13 years ago. Subsequent work by Mountcastle, Lynch and colleagues, Hyvarinen and colleagues, Robinson, Goldberg & Stanton, and Sakata and colleagues during the period of the late 1970s and early 1980s provided an informational and conceptual foundation for exploration of this fascinating area of the brain. Four new directions of research that are presently being explored from this foundation are reviewed in this article. 1. The anatomical and functional organization of the inferior parietal lobule is presently being investigated with neuroanatomical tracing and single cell recording techniques. This area is now known to be comprised of at least four separate cortical fields. 2. Neural mechanisms for spatial constancy are being explored. In area 7a information about eye position is found to be integrated with visual inputs to produce representations of visual space that are head-centered (the meaning of a head-centered coordinate system is explained on p. 13). 3. The role of the posterior parietal cortex, and the pathways projecting into this region, in processing information about motion in the visual world is under investigation. Visual areas within the posterior parietal cortex may play a role in extracting higher level motion information including the perception of structure-from-motion. 4. A previously unexplored area within the intraparietal sulcus has been found whose cells hold a representation in memory of planned eye movements. Special experimental protocols have shown that these cells code the direction and amplitude of intended movements in motor coordinates and suggest that this area plays a role in motor planning

How we see

The visual world is imaged on the retinas of our eyes. However, "seeing"' is not a result of neural functions within the eyes but rather a result of what the brain does with those images. Our visual perceptions are produced by parts of the cerebral cortex dedicated to vision. Although our visual awareness appears unitary, different parts of the cortex analyze color, shape, motion, and depth information. There are also special mechanisms for visual attention, spatial awareness, and the control of actions under visual guidance. Often lesions from stroke or other neurological diseases will impair one of these subsystems, leading to unusual deficits such as the inability to recognize faces, the loss of awareness of half of visual space, or the inability to see motion or color

Interior maps in posterior pareital cortex

The posterior parietal cortex (PPC), historically believed to be a sensory structure, is now viewed as an area important for sensory-motor integration. Among its functions is the forming of intentions, that is, high-level cognitive plans for movement. There is a map of intentions within the PPC, with different subregions dedicated to the planning of eye movements, reaching movements, and grasping movements. These areas appear to be specialized for the multisensory integration and coordinate transformations required to convert sensory input to motor output. In several subregions of the PPC, these operations are facilitated by the use of a common distributed space representation that is independent of both sensory input and motor output. Attention and learning effects are also evident in the PPC. However, these effects may be general to cortex and operate in the PPC in the context of sensory-motor transformations

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

In this proceedings we present a state-of-the-art method of calculating thermodynamic potential at finite temperature and finite chemical potential, using Hard Thermal Loop perturbation theory (HTLpt) up to next-to-next-leading-order (NNLO). The resulting thermodynamic potential enables us to evaluate different thermodynamic quantities including pressure and various quark number susceptibilities (QNS). Comparison between our analytic results for those thermodynamic quantities with the available lattice data shows a good agreement.Comment: 5 pages, 6 figures, conference proceedings of XXI DAE-BRNS HEP Symposium, IIT Guwahati, December 2014; to appear in 'Springer Proceedings in Physics Series

Simple stochastic models showing strong anomalous diffusion

We show that {\it strong} anomalous diffusion, i.e. \mean{|x(t)|^q} \sim t^{q \nu(q)} where $q \nu(q)$ is a nonlinear function of $q$, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically nu(2n) where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function P(x,t)=t^{-nu}F(x/t^nu) cannot hold, a part (sometimes) in the limit of very small x/t^\nu, now nu=lim_{q to 0} nu(q). Moreover the comparison with previous numerical results shows that the shape of F(x/t^nu) is not universal, i.e., one can have systems with the same nu but different F.Comment: Final versio