Large-field versus small-field expansions and Sobolev inequalities

1995 ◽  
Vol 79 (3-4) ◽  
pp. 525-568 ◽  
Author(s):  
Pirmin Lemberger
Keyword(s):  
Large Field ◽  
Sobolev Inequalities ◽  
Small Field ◽  
Field Versus

scholarly journals An Explicit Large Versus Small Field Multiscale Cluster Expansion

1997 ◽  
Vol 09 (02) ◽  
pp. 123-199 ◽  
Author(s):  
A. Abdesselam ◽  
V. Rivasseau
Keyword(s):  
Phase Space ◽  
Cluster Expansion ◽  
Large Field ◽  
Small Field ◽  
Field Versus ◽  
Multiscale Expansion ◽  
New Type ◽  
Renormalizable Theory ◽  
Model Independent ◽  
Text Model

We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the writing of explicit non-perturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared [Formula: see text] model as a testing ground. We used also a large field versus small field expansion. The polymer amplitudes, corresponding to graphs without almost local two and four point functions, are shown to satisfy the polymer bound.

Relation of cortical areas MT and MST to pursuit eye movements. III. Interaction with full-field visual stimulation

1988 ◽  
Vol 60 (2) ◽  
pp. 621-644 ◽  
Author(s):  
H. Komatsu ◽  
R. H. Wurtz
Keyword(s):  
Eye Movements ◽  
Visual Stimulation ◽  
Large Field ◽  
Field Stimulation ◽  
Small Field ◽  
Temporal Area ◽  
Pursuit Eye Movements ◽  
Preferred Direction ◽  
Small Spot ◽  
Spot Motion

1. Pursuit eye movements are usually made against a visual background that is moved across the retina by the pursuit movement. We have investigated the effect of this visual stimulation on the response of pursuit cells that lie within the superior temporal sulcus (STS) of the monkey. 2. We assigned these pursuit cells to one of two groups depending on the nature of their preferred visual stimulus. One group of cells, comprising all cells located in the dorsal-medial region of the medial superior temporal area (MSTd) and some cells in lateral-anterior MST (MST1), responded to the motion of a large patterned field but showed little or no response to small spots or slits. The other group, consisting of all foveal middle temporal area (MTf) cells and many MST1 cells, responded preferentially to small spot motion or equally well to small spot motion or large field. 3. For many pursuit cells that preferred large-field stimuli, the visual response showed a reversal of the preferred direction of motion as the size of the stimulus field increased. The reversal usually occurred as the size of the moving random-dot field used as a stimulus increased in size from 20 x 20 degrees to 30 x 30 degrees for motion at approximately 10 degrees/s. The size of the filed stimulus leading to reversal of preferred direction depended on the speed of stimulus motion. Higher speeds of motion required larger stimulus fields to produce a reversal of preferred direction. This reversal (of preferred direction) did not reflect a center-surround organization of the receptive field but seemed to reflect the spatial summation properties of these cells. 4. For three-quarters of the cells that preferred large-field stimulation, the preferred direction of motion for the large field was opposite to the preferred direction of the pursuit response. The remaining cells showed either the same preferred directions for large-field visual stimulation and the pursuit response or had bidirectional visual responses. If we consider only the cells that show a reversal of preferred direction for large- and small-field stimuli, the preferred direction for the large field was always the opposite to that of pursuit, and the preferred direction for the small field was always the same. 5. During pursuit against a lighted background, the cells that showed opposite preferred directions for large-field stimulation and pursuit had synergistic responses--a facilitation of the pursuit response over the response during pursuit in the dark. Slow pursuit speeds (less than 20 degrees/s) produced the greatest facilitation.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals The visual perception of plane tilt from motion in small field and large field: Psychophysics and theory

2006 ◽  
Vol 46 (20) ◽  
pp. 3494-3513 ◽  
Author(s):  
H. Zhong ◽  
V. Cornilleau-Pérès ◽  
L.-F. Cheong ◽  
G.M. Yeow ◽  
J. Droulez
Keyword(s):  
Visual Perception ◽  
Large Field ◽  
Small Field

scholarly journals PENGEMBANGAN MEDIA PENDIDIKAN UNTUK INOVASI PEMBELAJARAN DI PESANTREN

Edupedia ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 35-44
Author(s):  
Sukandi
Keyword(s):  
Learning Environments ◽  
Teaching And Learning ◽  
Field Trials ◽  
Learning Activities ◽  
Large Field ◽  
Small Field ◽  
Design Validation ◽  
Advantages And Disadvantages ◽  
The World ◽  
Enhance Student Learning

The increasingly dynamic development of information technology has implications for the world of education, especially learning activities. One of them by using media for helping the easy learning process that is very receive as benefit. Learning media can enhance student learning help to create joyful learning. But is not all learning media that can be applied in every learning environments, because learning media has advantages and disadvantages in several aspect. For the example is classical learning methods such as wetonan and bandongan become a characteristic teaching and learning activities in pesantren. Because of that, require a efforts to develop educational media suitably with the learning and the needs of students. Learning media development procedures iclude are potential and problems, data collection, product design, design validation, revision, small-field trials, revision, large-field trials, revision, massive production.

Dynamic properties of large-field and small-field optomotor flight responses in Drosophila

2007 ◽  
Vol 193 (7) ◽  
pp. 787-799 ◽  
Author(s):  
Brian J. Duistermars ◽  
Michael B. Reiser ◽  
Yan Zhu ◽  
Mark A. Frye
Keyword(s):  
Dynamic Properties ◽  
Large Field ◽  
Small Field

scholarly journals Neural circuit tuning fly visual interneurons to motion of small objects. I. Dissection of the circuit by pharmacological and photoinactivation techniques

1993 ◽  
Vol 69 (2) ◽  
pp. 329-339 ◽  
Author(s):  
A. K. Warzecha ◽  
M. Egelhaaf ◽  
A. Borst
Keyword(s):  
Visual Field ◽  
Moving Objects ◽  
Neural Circuit ◽  
Response Characteristic ◽  
Large Field ◽  
Small Field ◽  
Gamma Aminobutyric Acid ◽  
Ventral Part ◽  
Specific Selectivity

1. Visual interneurons tuned to the motion of small objects are found in many animal species and are assumed to be the neuronal basis of figure-ground discrimination by relative motion. A well-examined example is the FD1-cell in the third visual neuropil of blowflies. This cell type responds best to motion of small objects. Motion of extended patterns elicits only small responses. As a neuronal mechanism that leads to such a response characteristic, it was proposed that the FD1-cell is inhibited by the two presumably GABAergic and, thus, inhibitory CH-cells, the VCH- and the DCH-cell. The CH-cells respond best to exactly that type of motion by which the activity of the FD1-cell is reduced. The hypothesis that the CH-cells inhibit the FD1-cell and, thus, mediate its selectivity to small moving objects was tested by ablating the CH-cells either pharmacologically or by photoinactivation. 2. After application of the gamma-aminobutyric acid (GABA) antagonist picrotoxinin, the FD1-cell responds more strongly to large-field than to small-field motion, i.e., it has lost its small-field selectivity. This suggests that the tuning of the FD1-cell to small moving objects relies on a GABAergic mechanism and, thus, most likely on the CH-cells. 3. The role of each CH-cell for small-field tuning was determined by inactivating them individually. They were injected with a fluorescent dye and then ablated by laser illumination. Only photoinactivation of the VCH-cell eliminated the specific selectivity of the FD1-cell for small-field motion. Ablation of the DCH-cell did not significantly change the response characteristic of the FD1-cell. This reveals the important role of the VCH-cells in mediating the characteristic sensitivity of the FD1-cell to motion of small objects. 4. The FD1-cell is most sensitive to motion of small objects in the ventral part of the ipsilateral visual field, whereas motion in the dorsal part influences the cell only weakly. This specific feature fits well to the sensitivity of the VCH-cell to ipsilateral motion that is most pronounced in the ventral part of the visual field. The spatial sensitivity distribution of the FD1-cell matches also the characteristics of figure-ground discrimination and fixation behavior.

scholarly journals Gravitational wave spectra from oscillon formation after inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Takashi Hiramatsu ◽  
Evangelos I. Sfakianakis ◽  
Masahide Yamaguchi
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Parametric Resonance ◽  
Wave Spectrum ◽  
Large Field ◽  
Fluctuation Analysis ◽  
Small Field ◽  
Number Density ◽  
Peak Structure ◽  
Potential Shape

Abstract We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute both the properties of the emitted gravitational waves as well as the number density and characteristics of the produced oscillons. By performing numerical simulations for a variety of potential types, we divide the analyzed potentials in two families, each of them containing potentials with varying large- or small-field dependence. We find that the shape of the spectrum and the amplitude of emitted gravitational waves have a universal feature with the peak around the physical wavenumber k/a ∼ m at the inflaton oscillation starting period, irrespective of the exact potential shape. This can be used as a smoking-gun for deducing the existence of a violent preheating phase and possible oscillon formation after inflation. Despite this apparent universality, we also find differences in the shape of the spectrum of emitted gravitational waves between the two families of potentials, leading to discriminating features between them. In particular, all potentials show the emergence of a two-peak structure in the gravitational wave spectrum, arising at the time of oscillon formation. However, potentials that exhibit efficient parametric resonance tend to smear out this structure and by the end of the simulation the two-peak structure is replaced by one broad peak in the GW spectrum. We further compute the number density and properties of the produced oscillons for each potential choice, finding differences in the number density and size distribution of stable oscillons and transient overdensities. We also perform a linear fluctuation analysis and use the corresponding Floquet charts to relate the results of our simulations to the structure of parametric resonance for the various potential types. We find that the growth rate of the scalar perturbations and the associated oscillon formation time are sensitive to the small-field shape of a potential while the macroscopic physical properties of oscillons such as the total number depend on the large-field shape of a potential.

scholarly journals NATURAL INFLATION: STATUS AFTER WMAP THREE-YEAR DATA

2007 ◽  
Vol 16 (12b) ◽  
pp. 2573-2585 ◽  
Author(s):  
KATHERINE FREESE ◽  
WILLIAM H. KINNEY ◽  
CHRISTOPHER SAVAGE
Keyword(s):  
Early Universe ◽  
Classification Scheme ◽  
Accelerated Expansion ◽  
Large Field ◽  
Wilkinson Microwave Anisotropy Probe ◽  
Inflationary Cosmology ◽  
Small Field ◽  
Microwave Background ◽  
Scalar Spectral Index ◽  
Order Of Magnitude

Inflationary cosmology, a period of accelerated expansion in the early Universe, is being tested by cosmic microwave-background measurements. Generic predictions of inflation have been shown to be correct, and in addition individual models are being tested. The model of natural inflation is examined in light of recent three-year data from the Wilkinson Microwave Anisotropy Probe and shown to provide a good fit. The inflaton potential is naturally flat due to shift symmetries, and in the simplest version is V(ϕ) = Λ4 [1 ± cos (Nϕ/f)]. The model agrees with WMAP3 measurements as long as f > 0.7 m Pl (where m Pl = 1.22 × 1019 GeV ) and Λ ~ m GUT . The running of the scalar spectral index is shown to be small — an order of magnitude below the sensitivity of WMAP3. The location of the field in the potential when perturbations on observable scales are produced is examined; for f > 5 m Pl , the relevant part of the potential is indistinguishable from a quadratic, yet has the advantage that the required flatness is well motivated. Depending on the value of f, the model falls into the large field (f ≥ 1.5 m Pl ) or small field (f < 1.5 m Pl ) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.

Inflation and primordial perturbations

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Large Field ◽  
Inflationary Cosmology ◽  
Small Field ◽  
Quantum Field ◽  
Curved Space ◽  
Slow Roll ◽  
Starobinsky Model ◽  
Single Field

Review of inflationary cosmology. Single-field slow-roll inflation. Large-field inflation and small-field inflation. Starobinsky model. Quantum field theory in curved space. Generation of primordial perturbations during inflation. Mukhanov-Sasaki equation. Scalar and tensor perturbations.

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