Hippocampal ischemia causes deficits in local field potential and synaptic plasticity

The long-term enhancement in glutamate receptor mediated excitatory responses has been observed in stroke model. This pathological form of plasticity, termed post-ischemic long-term potentiation （i-LTP）, points to functional reorganization after stroke. Little is known, however, about whether and how this i-LTP would affect subsequent induction of synaptic plasticity. Here, we first directly confirmed that i-LTP was induced in the endothelin-l-induced ischemia model as in other in vitro models. We also demonstrated increased expression of NR2B, CaMKII and p-CaMKII, which are reminiscent of i-LTP. We further induced LTP of field excitatory post- synaptic potentials （fEPSPs） on CA1 hippocampal neurons in peri-infarct regions of the endothelin-l-induced mini-stroke model. We found that LTP of fEPSPs, induced by high-frequency stimulation, displayed a progressive impairment at 12 and 24 hours after ischemia. Moreover, using in vivo multi-channel recording, we found that the local field potential, which represents electrical property of cell ensembles in more restricted regions, was also dam- pened at these two time points. These results suggest that i-LTP elevates the induction threshold of subsequent synap- tic plasticity. Our data helps to deepen the knowledge of meta-synaptic regulation of plasticity after focal ischemia.

CALCULUS ON FRACTALS BASED UPON LOCAL FIELDS─In memory of Founding Editor Professor M.T.Cheng with great respect and deep sorrow

The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE on fractals.

Some New Inequalities for Wavelet Frames on Local Fields

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.

Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules

This paper investigates the effect of Lorentz local field correction （LFC） on the propagation of ultrashort laser pulses in a para-nitroaniline molecular medium under resonant and nonresonant conditions by solving numerically the full-wave Maxwell-Bloch equations beyond slowly-varying envelope approximation and rotating-wave approximation. The effect of the LFC is considerably obvious when pulses with large areas propagate in the dense molecular medium. In the case of resonance, the group velocity of the sub-pulses split from the incident pulse along propagation is severely decreased by the LFC, especially for the latest sub-pulse. However, in the case of nonresonance, the influence of the LFC on the temporal evolution of the pulse is less obvious and lacks homogeneity with an increase in incident pulse area, propagation distance and molecular density.

Simultaneous low extinction and high local field enhancement in Ag nanocubes

We theoretically investigate surface plasmon resonance properties in Au and Ag cubic nanoparticles and find a novel plasmonic mode that exhibits simultaneous low extinction and high local field enhancement properties. We analyse this mode from different aspects by looking at the distribution patterns of local field intensity, energy flux, absorption and charge density. We find that in the mode the polarized charge is highly densified in a very limited volume around the corner of the nanocube and results in very strong local field enhancement. Perturbations of the incident energy flux and light absorption are also strongly localized in this small volume of the corner region, leading to both low absorption and low scattering cross section. As a result, the extinction is low for the mode. Metal nanoparticles involving such peculiar modes may be useful for constructing nonlinear compound materials with low linear absorption and high nonlinearity.

Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.

ON RIESZ TYPE KERNELS OVER LOCAL FIELDS

Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp boundedness of such operators motivated by the open problem: Does σηfa,s→f for f ∈L1(O) (see M. H. Taible-son [6] and [5])?

Effect of focused ultrasound stimulation at different ultrasonic power levels on the local field potential power spectrum

Local field potential(LFP) signals of the rat hippocampus were recorded under noninvasive focused ultrasound stimulation(FUS) with different ultrasonic powers. The LFP mean absolute power was calculated with the Welch algorithm at the delta, theta, alpha, beta, and gamma frequency bands. The experimental results demonstrate that the LFP mean absolute power at different frequency bands increases as the ultrasound power increases.

LOCAL HARDY SPACES ON HEISENBERG GROUP OVER LOCAL FIELDS

Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.

CHAINS OF FUNCTION SPACES OVER EUCLIDIAN SPACES AND LOCAL FIELDS

The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.

ON HAUSDORFF DIMENSION OF CERTAIN RIESZ PRODUCT IN LOCAL FIELDS

In this paper, we consider the Riesz product dμ =^∞∏j=1（1＋ajRexbjλj（x））dx in local fields, and we obtain the upper and lower bound of its Hausdorff dimension.

Effect of propofol on local field potential in rat prefrontal cortex during working memory task

Propofol may produce memory impairment during anesthesia procedure. Local field potentials (LFPs) are used with increasing frequency in recent years to link neural activity to perception and cognition. In this study, effect of propofol on LFPs in rat’s prefrontal cortex during working memory task was evaluated. Young (approximately 3 month) male Sprague-Dawley rats were divided into two group: propofol rats and control rats. Propofol rats received propofol at 0.9 mg/Kg·min intravenously for 2 h. After 12 h, LFPs of all rats were measured simultaneously from multiple electrodes placed in prefrontal cortex while rats were performing a working memory task in Y-maze. LFPs instantaneous phase were obtained by applying Hilbert transform, and cross-correlation coherence of LFPs was calculated. The results indicate that propofol decreased the correct rate and crosscorrelation coherence of LFPs on the first two days (p 0.05). Our results suggest that propofol can impair cross-correlation coherence of LFPs in the first two days, but not long time.

Local field distribution and configuration of CO molecules adsorbed on the nanostructure platinum surface

This paper shows that the local electric field distribution near the nanostructure metallic surface is obtained by solving the Laplace equation, and furthermore, the configuration of CO molecules adsorbed on a Pt nanoparticle surface is obtained by using Monte Carlo simulation. It is found that the uneven local electric field distribution induced by the nanostructure surface can influence the configuration of carbon monoxide （CO） molecules by a force, which drags the adsorbates to the poles of the nanoparticles. This result, together with our results obtained before, may explain the experimental results that the nanostructure metallic surface can lead to abnormal phenomena such as anti-absorption infrared effects.

On Characterization of Nonuniform Tight Wavelet Frames on Local Fields

In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.

Slow Gamma Activity of Local Field Potentials (LFP) in the Freely Moving Rat Relates to Movement

Quantitative assessment of local field potentials by means of Fast Fourier Transformation (FFT) results in the so-called power density spectrum. Within this spectrum particular frequency ranges are defined in order to relate these to behavior. Frequencies above 35 Hz are generally labeled as gamma oscillations, especially as low gamma (40 - 55 Hz) or high gamma (70 - 100 Hz). In order to learn more about this feature, we implanted a set of 4 bipolar concentric steel electrodes in frontal cortex, hippocampus, striatum and midbrain reticular formation of 10 rats. After recovery, field potentials were recorded and wirelessly transmitted to our computer for frequency analysis. At the same time, motion was registered during the whole experimental period of 5.75 hours. Results revealed that low gamma activity only emerged when the animal moved—at least his head. FFT of the data showed—besides other frequencies—a slow gamma activity peaking around 47 Hz pre-dominantly within the striatum, less in frontal cortex and reticular formation and nearly none in the hippocampus. Spectral analysis was performed for single epochs of 4 seconds and all 15 minutes intervals. Correlation analysis of these intervals was done to motion data. All rats showed a highly significant correlation between gamma activity and movement. We therefore conclude from these experiments that this slow gamma activity of the field potentials is not only related to movement, but possibly part of the general neuronal coding of movement.

The role of local field potential coupling in epileptic synchronization

This review hopes to clearly explain the following viewpoints： （1） Neuronal synchronization underlies brain functioning, and it seems possible that blocking excessive synchronization in an epileptic neural network could reduce or even control seizures. （2） Local field potential coupling is a very common phenomenon during synchronization in networks. Removal of neurons or neuronal networks that are coupled can significantly alter the extracellular field potential. Interventions of coupling mediated by local field potentials could result in desynchronization of epileptic seizures. （3） The synchronized electrical activity generated by neurons is sensitive to changes in the size of the extracellular space, which affects the efficiency of field potential transmission and the threshold of cell excitability. （4） Manipulations of the field potential fluctuations could help block synchronization at seizure onset.

Tunable multiple plasmon resonances and local field enhancement of nanocrescent/nanoring structure

According to the plasmon hybridization theory, the plasmon resonance characteristics of the gold nanocrescent/nanoring(NCNR) structure are systematically investigated by the finite element method. It is found that the extinction spectra of NCNR structure exhibit multiple plasmon resonance peaks, which could be attributed to the result of the plasmon couplings between the multipolar plasmon modes of nanocrescent and the dipolar, quadrupolar, hexapolar, octupolar,decapolar plasmon modes of nanoring. By changing the geometric parameters, the intense and separate multiple plasmon resonance peaks are obtained and can be tuned in a wide wavelength range. It is further found that the plasmon coupling induces giant multipole electric field enhancements around the tips of the nanocrescent. The tunable and intense multiple plasmon resonances of NCNR structure may provide effective applications in multiplex biological sensing.

Local field potentials,spiking activity,and receptive fields in human visual cortex

The concept of receptive field(RF) is central to sensory neuroscience. Neuronal RF properties have been substantially studied in animals,while those in humans remain nearly unexplored. Here, we measured neuronal RFs with intracranial local field potentials(LFPs) and spiking activity in human visual cortex(V1/V2/V3). We recorded LFPs via macro-contacts and discovered that RF sizes estimated from lowfrequency activity(LFA, 0.5–30 Hz) were larger than those estimated from low-gamma activity(LGA, 30–60 Hz) and high-gamma activity(HGA, 60–150 Hz). We then took a rare opportunity to record LFPs and spiking activity via microwires in V1 simultaneously. We found that RF sizes and temporal profiles measured from LGA and HGA closely matched those from spiking activity. In sum, this study reveals that spiking activity of neurons in human visual cortex could be well approximated by LGA and HGA in RF estimation and temporal profile measurement, implying the pivotal functions of LGA and HGA in early visual information processing.

Strong field ionization of molecules on the surface of nanosystems

Besides the diverse investigations on the interactions between intense laser fields and molecular systems,extensive research has been recently dedicated to exploring the response of nanosystems excited by well-tailored femtosecond laser fields.Due to the fact that nanostructures hold peculiar effects when illuminated by laser pulses,the underlying mechanisms and the corresponding potential applications can make significant improvements in both fundamental research and development of novel techniques.In this review,we provide a summarization of the strong field ionization occurring on the surface of nanosystems.The molecules attached to the nanoparticle surface perform as the precursor in the ionization and excitation of the whole nanosystem,the fundamental processes of which are yet to be discovered.We discuss the influence on nanoparticle constituents,geometric shapes and sizes,as well as the specific waveforms of the excitation laser fields.The intriguing characteristics observed in surface ion emission reflect how enhanced near field affects the localized ionizations and nanoplasma expansions,thereby paving the way for further precision controls on the light-and-matter interactions in the extreme spatial temporal levels.

Lipschitz classes on local fields

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).