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PubMed1988

Neural mechanisms of absolute tactile localization in monkeys.

Macaca nemestrina monkeys were trained to indicate the location of suprathreshold tactile stimuli delivered to the glabrous skin of either foot. The testing paradigm involved self-initiated trials (a bar press), followed by 10-Hz stimulation at one of six locations (e.g., on the distal phalanx of the second toe on the left foot), providing the opportunity for the animal to press one of six buttons located on a facing panel. The buttons were positioned on a picture of a monkey's feet at locations corresponding to the skin loci that were stimulated on different trials. If the animal first pressed the button corresponding to the position stimulated, liquid reward was delivered; responses to any other button terminated stimulation without reward, requiring initiation of another trial for the opportunity to receive reinforcement. The localization errors for normal monkeys were reliably greater along the mediolateral dimension of the foot than they were proximodistally. For example, stimulation of the tip of toe 4 elicited responses to the button at the tip of toe 2 on 25% of the trials, as compared with only 10% errors between the tip of toe 4 and the pad at the base of toe 4. Following unilateral interruption of the dorsal spinal columns at an upper thoracic level, the capacity for absolute tactile localization was unchanged over months of testing. The greater localization accuracy along the proximodistal axis of the foot remained after dorsal column transection. In order to evaluate neural substrates of localization by monkeys, single-neuron receptive field (RF) sizes and distributions within the first somatosensory (SI) cortex were examined to determine the overlap or separation of the representations of different points on glabrous skin. The sample of neurons that provided the RF data was obtained in previous investigations of unanesthetized, neuromuscularly blocked Macaca fascicularis monkeys. Analysis of RF overlap revealed that greater than 50% of cytoarchitectural area 1 units that responded to stimulation of one digit tip also responded to another digit or to the pad at the base of a digit. These large RFs seem poorly suited to subserve a high degree of spatial localization and are compatible with the frequent localization errors by the monkeys in the behavioral experiments. However, the area 1 RF data do not explain the tendency of these animals to exhibit better localization accuracy along the proximodistal axis than along the mediolateral axis of the volar foot.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2006

Localized excitation in the hybridization gap in YbAl3.

The intermediate valence compound YbAl3 exhibits a broad magnetic excitation in the inelastic neutron scattering spectrum with characteristic energy E1 approximately 50 meV, equal to the Kondo energy (T(K) approximately 600-700 K). In the low temperature (T < T(coh) approximately 40 K) Fermi liquid state, however, a new peak in the scattering occurs at E2 approximately 33 meV, which lies in the hybridization gap that exists in this compound. We report inelastic neutron scattering results for a single-crystal sample. The scattering at energies near E1 qualitatively has the momentum (Q) dependence expected for interband scattering across the indirect gap. The scattering near E2 has a very different Q dependence: it is a weak function of Q over a large fraction of the Brillouin zone and is smallest near (1/2,1/2, 1/2). A possibility is that the peak at E2 arises from a spatially localized excitation in the hybridization gap.

Journal Article↗
PubMedDate not supplied

Evoked magnetic responses of the human auditory cortex to minor pitch changes: localization of the mismatch field.

The neuromagnetic source localizations of the auditory M100 and the mismatch field (MMF) were studied using a large-array biomagnetometer. Standard tones of 1000 Hz and deviant tones of 1050 Hz were delivered with 90% and 10% probability, respectively. Wave forms of the derived MMF were computed by examining difference wave forms between the responses to the deviants and the responses to the standards preceding (D-P) and following (D-F) the deviants as well as to all remaining standards (D-A). The subset of standards preceding the deviants was used for a more realistic comparison with the set of deviants (having the same number of epochs and a similar signal-to-noise ratio), while the subset of standards following the deviants served to answer the question whether those standards also elicit an MMF. The MMF deflections were compared with each other, with the "native" MMF occurring in response to the deviants, and with wave M100. (The MMF as it appears in the unprocessed response to the deviants was termed "native" for an easy distinction from the "derived" MMF.) Our results demonstrate a distinct MMF deflection, corresponding in latency to the simultaneously recorded fronto-central electrical MMN. Source analysis, using a single moving dipole model, showed the same spatial localization for the native MMF and for the different derived MMFs. The MMF source location turned out to be significantly anterior, medial and inferior relative to the sources of the M100. The present data also demonstrate that a minor frequency deviation may not activate measurably different M100 generators, yet be sufficient to trigger the nearby but spatially distinct mismatch generator.

Acoustic Stimulation↗
PubMed2006

Photonic activation of disulfide bridges achieves oriented protein immobilization on biosensor surfaces.

Photonic induced immobilization is a novel technology that results in spatially oriented and spatially localized covalent coupling of biomolecules onto thiol-reactive surfaces. Immobilization using this technology has been achieved for a wide selection of proteins, such as hydrolytic enzymes (lipases/esterases, lysozyme), proteases (human plasminogen), alkaline phosphatase, immunoglobulins' Fab fragment (e.g., antibody against PSA [prostate specific antigen]), Major Histocompability Complex class I protein, pepsin, and trypsin. The reaction mechanism behind the reported new technology involves "photonic activation of disulfide bridges," i.e., light-induced breakage of disulfide bridges in proteins upon UV illumination of nearby aromatic amino acids, resulting in the formation of free, reactive thiol groups that will form covalent bonds with thiol-reactive surfaces (see Fig. 1). Interestingly, the spatial proximity of aromatic residues and disulfide bridges in proteins has been preserved throughout molecular evolution. The new photonic-induced method for immobilization of proteins preserves the native structural and functional properties of the immobilized protein, avoiding the use of one or more chemical/thermal steps. This technology allows for the creation of spatially oriented as well as spatially defined multiprotein/DNA high-density sensor arrays with spot size of 1 microm or less, and has clear potential for biomedical, bioelectronic, nanotechnology, and therapeutic applications.

Antibodies, Monoclonal↗
PubMed1998

Radionuclide scanning in parathyroid diseases.

BACKGROUND: New radionuclide agents and scanning procedures have markedly improved preoperative parathyroid gland localization. The aim of this review was to evaluate the results of parathyroid scanning and to clarify its current place in the clinical management of parathyroid diseases. METHODS: The literature describing the different radioisotopes and available scanning techniques was analysed and their clinical outcome in various parathyroid diseases was evaluated. RESULTS: Using 99mTc-radiolabelled sestamibi or other 9mTc-labelled cationic complexes, parathyroid scintigraphy detects 87 per cent of solitary adenomas (n=894), 55 per cent of abnormal glands in patients with multiglandular disease (n=303) and 75 per cent of persistent or recurrent lesions in patients with previous neck surgery (n=240). If necessary, three-dimensional imaging techniques can clarify the spatial localization of an ectopic uptake focus. The positive predictive value of the available scanning procedures is over 95 per cent, but false-positive uptake may be encountered. CONCLUSION: Radionuclide parathyroid gland scanning with 99mTc-labelled cationic complexes is the initial non-invasive method of choice for preoperative parathyroid gland localization in patients at special risk and/or with previous neck exploration. While scanning has also been proposed to facilitate parathyroidectomy, there is no objective evidence to support its routine use before a first-time surgical procedure.

False Positive Reactions↗
PubMed2005

CD80 cytoplasmic domain controls localization of CD28, CTLA-4, and protein kinase Ctheta in the immunological synapse.

The binding of costimulatory ligand CD80 to CD28 or CTLA-4 on T cells plays an important role in the regulation of the T cell response. We have examined the role of the cytoplasmic domain of CD80 in murine T cell costimulation and its organization in the immunological synapse (IS). Removal of CD80 cytoplasmic tail decreased its effectiveness in costimulating T cell proliferative response and early IL-2 production in response to agonist MHC-peptide complexes. Immunofluorescent study showed a decreased tailless CD80 accumulation in the IS of naive T cells. The two forms of CD80 accumulated differently at the IS; the tailless CD80 was colocalized with the TCR whereas the full-length CD80 was segregated from the TCR. In addition, we showed that CD80, CD28, and protein kinase Ctheta colocalized in the presence or absence of the CD80 cytoplasmic tail. Thus, the cytoplasmic tail of CD80 regulates its spatial localization at the IS and that of its receptors and T cell signaling molecules such as protein kinase Ctheta, and thereby facilitates full T cell activation.

Animals↗
PubMed2002

Acoustic propagation through anisotropic internal wave fields: transmission loss, cross-range coherence, and horizontal refraction.

Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is interpreted as a nonstationary oceanographic waveguide within the water column, preferentially funneling acoustic energy between the thermocline depressions.

Acoustics↗
PubMed2006

2D partially parallel imaging with k-space surrounding neighbors-based data reconstruction.

Partially parallel imaging (PPI) achieves imaging acceleration by replacing partial phase encoding (PE) with the spatially localized sensitivity encoding of a receiver surface coil array. Further accelerations can be achieved through 2D PPI along two PE directions in 3D MRI. This paper is to explore the k-space-based PPI acquisition and reconstruction strategies for 3D MRI. A surrounding neighbors-based autocalibrating PPI (SNAPPI) was first presented by generalizing the 2D multicolumn multiline interpolation method. Several 2D PPI reconstruction methods were then provided by applying SNAPPI to recover the partially skipped k-space data along two PE directions separately or nonseparately, in k-space or in the hybrid k and image space. An optimal 2D PPI sampling-based reconstruction approach was also presented for applying PPI along certain spatial direction along which the array coil has not sufficient sensitivity variation for a valid PPI reconstruction. Both simulated and in vivo 2D PPI data were used to evaluate the proposed methods.

Algorithms↗
PubMed2000

EEG correlates of finger movements as a function of range of motion and pre-loading conditions.

OBJECTIVES: The present study was designed to obtain additional data regarding the differential influence of kinematic parameters and different nominal force levels upon components of movement-related cortical potentials (MRP) during index finger flexion. METHODS: The absolute nominal force level of discrete movements was varied while the rate of force development remained constant within a given task. This was accomplished by utilizing a pre-loading experimental design at different ranges of index finger motion (25, 50 and 75 degrees), so that the movement kinematic profiles (velocity and acceleration) and rate of force development remained constant within each given range of motion. Time-domain averaging of EEG single trials was applied in order to extract 3 movement-related potentials (BP(-600 to -500), BP(-100 to 0) and N(0 to 100)) preceding and accompanying 25, 50 and 75 degrees of unilateral finger movement with no pre-load (0 g), small pre-load (100 g) and large pre-load (200 g). RESULTS: The range of motion differentially influenced the amplitude of early (BP(-600 to -500)) and late (BP(-100 to 0)) MRP components spatially localized over frontal, central and parietal areas. The amplitude of the N(0 to 100) component localized over parietal and frontal areas was also sensitive toward experimental manipulations of the range of motion. Overall, the amplitude of N(0 to 100) localized over the central area was the only MRP component that was sensitive to the amount of pre-loading. However, within a given range of motion, none of the pre-loading conditions (0, 100 or 200 g) influenced the amplitude of MRP components. CONCLUSIONS: The central finding was that an increase in nominal force production within a given range of motion did not influence MRP components when the rate of force development was held constant. It becomes especially apparent with strict control of kinematic and kinetic movement parameters that different methods of adding weight to the index finger performing the same movement patterns have different consequences for EEG correlates as reflected in the amplitude and spatial distribution of MRP. The range of motion of index finger flexion was the primary kinematic variable that consistently influenced MRP components both preceding and accompanying movement execution.

Adult↗
PubMed1998

Cytochemistry of the functional domains of the nucleus in normal and in pathologic conditions.

By means of ultrastructural cytochemistry significant advances have been made in understanding the functional roles of many nuclear domains. This review gives schematic information about the main nuclear domains involved in replication, transcription, processing and transport of the transcripts in normal and in pathologic conditions. Particular attention is paid to a functional domain that appears to be involved in signal transduction. Data are reported on the intranuclear specific localization of key elements of the polyphosphoinositide signal transduction system in different cell types including human osteosarcoma cell lines. Compared with the compartmentalization of the cytoplasm, the nucleus has long been considered as relatively unstructured. On the other hand, fundamental nuclear functions, such as DNA replication and RNA transcription, can be molecularly characterized also in cell-free systems, suggesting that supramolecular organization is not so strictly required as for other cell functions occurring within intact cytoplasmic organelles. Nevertheless, a stringent organization is required for packing about 200 cm of DNA in the about 30 micron 3 of the nucleus. In the absence of membrane-delimited organelles, the nuclear organization is based on functional compartments, or domains, whose spatial localization involves the nuclear matrix, which shares many properties with the cytoskeleton. The nuclear domains are defined as structural compartments, not necessarily stable but dynamically variable, which perform specific metabolic functions through the partitioning of molecular complexes. Their identification has been made possible in the last few years by the development of specific nuclear probes for confocal and electron microscope immunocytochemistry. Therefore, the complex network of structures and enzymatic functions that make up the nucleus is in several cases yielding to molecular analysis, but a large part remains unknown (Strouboulis and Wolffe, 1996; Laemmli and Tjian, 1996). Rapid advances in understanding the functional role of the nuclear domains have been made recently: in particular, of the nuclear envelope, of the nucleolus, and of RNA splicing. In other cases, e.g. the precise localization of the nuclear domains involved in signal transduction, much remains to be clarified (Forbes and Johnson, 1997). It is conceivable that in the near future unexpected new nuclear domains will come to light and new nuclear functions may emerge, especially in field of post-transcriptional processing and transport of RNAs, and in the relationships between the nucleo-skeleton and enzymic fixed sites involved in replication, transcription and signal transduction. The aim of this review is to provide information about the morphological characteristics, the associated functions and the molecular composition of the main nuclear domains found to date. To simplify the exposition, the main data on each nuclear domain are reported in Tables, together with the principal references on the subject. Figures refer to original findings on some aspects of nuclear domain organization.

Cell Nucleus↗
PubMed2003

Dynamic distribution of epidermal growth factor during mouse embryo peri-implantation.

Embryo implantation depends on the synchronized development of the blastocyst and the endometrium. This process is highly controlled by the coordinated action of the steroid hormones: estrogen and progesterone. By autocrine, paracrine or juxtacrine routes, some growth factors or cytokines are involved in this steroidal regulation pathway. Here we report the effects of epidermal growth factor (EGF) on embryo implantation in the mouse, the expression and distribution patterns of EGF protein in the mouse blastocyst, ectoplacental cone (EPC) and peri-implantation uterus on days 1-8 of gestation. By RT-PCR and dot blot, we found that EGF and its receptor (EGFR) are co-expressed in the blastocyst and peri-implantational uteri of pregnant days 2-8 (D2-D8) mice. Injection of EGF antibody into a uterine horn on the third day of pregnancy (D3) significantly reduced the number of mouse embryos that implanted on D8, indicating EGF have a function in the mouse embryo implantation.Further investigation by using indirect immunofluorescence and confocal microscope was made to trace EGF and EGFR protein localization during the mouse embryo implantation. EGF and EGFR are co-localized in the blastocyst, and in the secondary trophoblastic giant cells (SGC) of the EPC. At the pre-implantation stage, the distribution of EGF protein in the mouse uterus changes from epithelium to stroma. On D1 of pregnancy, EGF is mainly distributed in uterine stroma and myometrium. On D2, it is present in the uterine epithelium. On D3, it changes again from the uterine epithelium to the stroma. By D4, EGF is predominantly in the stroma. This dynamic distribution correlates with the proliferation activity of uterine cells at each period. On D6-D8 of embryo implantation, EGF 3 protein accumulates at the uterine mesometrial pole, a region that contributes to the trophoblastic invasiveness and placentation. This temporal and spatial localization of EGF protein in the mouse uterus implicates the cytokine in the regulation of trophoblastic invasiveness and uterine receptiveness.

Animals↗
PubMed1995

Distance cues for vertical vergence adaptation.

Vertical vergence can be trained to respond to vertical and/or horizontal conjugate eye position, horizontal vergence, and vertical head tilt. This cross-coupling is manifest as a vertical phoria aftereffect (monocular vertical vergence response) that varies with direction and distance of gaze. The function of the spatially dependent adaptation is to maintain the calibration between vertical eye alignment and intended placement of the two retinal images. Oculomotor adaptation stabilizes our sense of spatial localization and calibrates a body-referenced coordinate representation of visual space that is necessary for visually guided motor responses. We have tested the possible association of vertical phoria adaptation with perceptual cues to distance in the absence of any other associated motor activity. During adaptive training, vertical disparity vergence was associated with variations of perceptual distance cues (including loom, overlap, relative size, and relative motion), oculomotor distance cues (horizontal vergence), or a combination of both classes of cues. We observed that in a 2-h period the open-loop (monocular) vertical vergence response could not be trained to occur as an aftereffect in association with the perceptual cues to distance, whereas it could be trained in association with oculomotor cues. We conclude that the spatial specificity of vertical vergence aftereffects caused by short-term adaptation results from an associated cross-coupling with supranuclear sources of oculomotor activity.

Adaptation, Ocular↗
PubMed2003

Cellular distribution of lens epithelium-derived growth factor (LEDGF) in the rat eye: loss of LEDGF from nuclei of differentiating cells.

Lens epithelium-derived growth factor (LEDGF) enhances the survival and growth of cells. To understand LEDGF's spatial localization and its putative function(s) during proliferation and differentiation, we localized LEDGF during terminal differentiation in whole rat lenses, lens epithelial cell (LEC) explants stimulated with FGF-2, and insulin, iris, human LECs with lentoids. In addition, intracellular localization of LEDGF was performed in other ocular tissues: ciliary body, retina, and cornea. We found the immunopositivity of nuclear LEDGF decreased in LECs of the equatorial region. In contrast, immunopositivity of LEDGF was detected in the cytoplasm of LECs and superficial fiber cells. After treating LEC explants with FGF-2 and insulin, which are known to be differentiating factors for LECs, the nuclei of these cells showed no LEDGF immunopositivity, but explants did express p57(kip2), a differentiation marker protein. Also, immunopositive LEDGF was not detected in the nuclei of differentiated cells, lentoid body, and corneal epithelial cells. This demonstrated that the loss of LEDGF from the nucleus may be associated with the process of terminal differentiation that might be in some way common with the biochemical mechanisms of apoptosis. The spatial and temporal distribution of LEDGF in the present study also provides a vision for further investigation as to how this protein is involved in cell fate determination.

Animals↗
PubMed2007

"Sequence Agnosia" in Bálint's syndrome: defects in visuotemporal processing after bilateral parietal damage.

Bálint's syndrome is characterized by visuospatial dysfunction, with failure to attend to multiple objects in space and poor spatial localization manifested as impaired reaching and saccadic targeting. Less investigated in this disorder is perceptual processing along the dimension of time. We studied the performance of a patient with Bálint's syndrome on two oddity paradigms in which she had to indicate which of three objects was different in color, shape, or structure. Her initial difficulty with processing multiple objects present simultaneously in different locations recovered, but she had persistent difficulty processing objects seen sequentially at the same location. Further studies showed that this deficit was not due to impairments in sustained attention or in distributing attention over time, but to impaired processing of temporal sequences. The deficit was also present with auditory stimuli, indicating a multimodal failure of temporal sequencing. These findings show that bilateral parietal lesions affect not only the spatial but also the temporal organization of perception.

Agnosia↗
PubMed2002

Contrast-enhanced three-dimensional transcranial color-coded sonography of intracranial stenoses.

BACKGROUND AND PURPOSE: Intracranial stenoses are associated with a considerable number of strokes each year. The clinical value of a workstation-based three-dimensional (3D) reconstruction system for transcranial color-coded sonography was evaluated in patients with intracranial stenosis or occlusion. METHODS: Twenty-six patients (13 men, 13 women; mean age, 57 years +/- 12 [SD]) with 36 intracranial stenoses or occlusions, as detected at two-dimensional (2D) color Doppler imaging (CDI) and digital subtraction angiography (DSA), underwent Levovist-enhanced power Doppler imaging (PDI), with subsequent 3D reconstruction. A workstation connected to a magnetic sensor capable of spatial localization of the probe was used to reconstruct 3D images of the circle of Willis from serial PDI images. RESULTS: At DSA, seven (19%) stenoses were estimated to less than 50%, 24 (67%) were 50% or more, and five (14%) were occluded. DSA and 3D-PDI estimates of the degree of stenosis agreed in 33 cases (92%), with a weighted kappa value of 0.86. Disagreement occurred with two subtotal basilar artery stenoses and one subtotal middle cerebral artery stenosis, which were evaluated as being complete occlusions at 3D-PDI. Interobserver agreement between two experienced 3D investigators in estimating the percentage of stenosis was high (correlation coefficient,.98). CONCLUSION: 3D-PDI enables the investigator to reconstruct virtually any arbitrary viewing angle. Compared with conventional CDI, 3D-PDI offers easier spatial assessment of intracranial stenoses, and its findings are sufficiently correlated with angiographic findings. Because different investigators can postprocess the same 3D data, improving reproducibility and reducing investigator dependency in transcranial color-coded sonography may be possible.

Aged↗
PubMed2004

Energy thresholds for discrete breathers.

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. An important issue, not only from a theoretical point of view but also for their experimental detection, is their energy properties. We considerably enlarge the scenario of possible energy properties presented by Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]]. Breather energies have a positive lower bound if the lattice dimension is greater than or equal to a certain critical value dc. We show that dc can generically be greater than 2 for a large class of Hamiltonian systems. Furthermore, examples are provided for systems where discrete breathers exist but do not emerge from the bifurcation of a band edge plane wave. Some of these systems support breathers of arbitrarily low energy in any spatial dimension.

Journal Article↗
PubMed1996

Dissociation of hippocampal and striatal contributions to spatial navigation in the water maze.

Two experiments were conducted to compare the effects of fornix/fimbria and caudate-putamen lesions in Long-Evans hooded rats (Rattus norvegicus) trained on two water maze tasks that differed in the type of spatial localization required for optimum solution. In Experiment 1, the lesioned rats and surgical controls were trained on the standard place task in the water maze (Morris, 1981) and given two postacquisition tests (a platform removal probe and platform relocation test). In Experiment 2, rats with similar lesions and control rats were trained on a modified cue navigation task. Fornix/fimbria lesions impaired a late stage of place task acquisition but did not impair acquisition of the cue task. Caudate-putamen lesions resulted in a severe place acquisition impairment and a transient cue acquisition impairment, both of which were characterized by an initial tendency to swim near the wall of the pool. Post-hoc analyses of the direction and angles of departure from the start points suggested that rats with fornix/fimbria lesions used non-allocentric spatial strategies to solve the place task. These rats also demonstrated a significantly weakened spatial bias for the former training quadrant on the platform removal probe and reduced flexibility in navigating to a novel platform location on the platform relocation test. In contrast, rats with caudate-putamen lesions showed a significant spatial bias for the former training quadrant but failed to cross the exact location within the quadrant where the platform was formerly positioned. The results suggest that the hippocampus mediates the allocentric spatial component of the water maze place task while the dorsomedial striatum may play an important role in the acquisition of the procedural aspects of both place and cue versions of the task.

Animals↗
PubMed1999

Breathers and multibreathers in a periodically driven damped discrete nonlinear Schrödinger equation.

We study an integrable discretization of the nonlinear Schrödinger equation (NLS) under the effects of damping and periodic driving, from the point of view of spatially localized solutions oscillating in time with the driver's frequency. We locate the equilibrium states of the discretized (DNLS) system in the plane of its dissipation gamma and forcing amplitude H parameters and use a shooting algorithm to construct the desired solutions psi(n)(t)=phi(n) exp(it) as homoclinic orbits of a four-dimensional symplectic map in the complex phi(n),phi(n+1) space, for -infinity<n<infinity. We derive, in the gamma=0 case, closed form expressions for two fundamental such solutions having a single hump in n, psi(n)+, and psi(n)-, and determine analytically their threshold of existence in the (gamma,H) plane using Mel'nikov's theory. Then, we demonstrate numerically that above this threshold a remarkable variety of multihump structures appear, whose complexity in terms of their spatial extrema grows with increasing H. All these solutions are numerically found to be unstable in time, except for psi(n)-, which is seen to be stable over a certain region in the (gamma,H) plane. In the continuum limit our results are in close agreement with recent studies on the NLS equation. From a more general perspective, we view these DNLS multihump solutions as homoclinic orbits of a higher-dimensional map thereby providing a possible mechanism for explaining the occurrence of similar structures called discrete (multi-) breathers found in a wide variety of one-dimensional nonlinear lattices.

Journal Article↗