Hippocampal Theta

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Neurochemical Modulation Frequency Band of
Hippocampal Theta Rhythm

Neurochemical Modulation Frequency Band of Hippocampal Theta Rhythm

In recent experimental studies have shown that the medial septum nucleus receives phases already encoded information from the uplink system, the frequency of which determines and the frequency of discharges of the hippocampal theta rhythm. There is evidence that this information comes from the supramammilyar nucleus of the hypothalamus [8]. Our research has previously been shown that the destruction of Dorsal

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Modulation of synaptic plasticity by hippocampal theta rhythm

Modulation of synaptic plasticity by hippocampal theta rhythm

Physiological regulators of synaptic plasticity remain unknown, but hippocampal theta rhythm is a proposed candidate. The hippocampal theta rhythm represents a rhythmic oscillation in membrane potential ranging from 3-10 Hz. The significance of theta rhythm originates from its association with active behaviors in rodents such as walking, rearing, and spatial exploration (Leung, 1998; Vanderwolf, 1969). During awake-immobility and slow-wave sleep, irregular slow activity (ISA) with delta and slow oscillations predominate the EEG (Leung et al., 1982; Wolansky et al., 2006). Theta rhythm can be broadly classified into two categories: Type I (atropine-resistant) and Type II (atropine- sensitive). Type I or movement theta occurs during certain kinds of movements (e.g., walking, head movements, jumping, swimming, and other voluntary movements). It also occurs during phasic periods of REM sleep and is distinguished by its ability to be unaffected by large doses of atropine. Type II or immobility theta occurs during certain motionless behaviours, where the animal's attention is engaged, and is abolished by large doses of atropine. Atropine-sensitive theta rhythm is also present during urethane- anaesthesia and can either be spontaneous or induced using a strong sensory stimuli. Atropine-sensitive theta typically has a lower frequency than atropine-resistant theta.
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Respiratory cycle entrainment of septal neurons mediates the fast coupling of sniffing rate and hippocampal theta rhythm

Respiratory cycle entrainment of septal neurons mediates the fast coupling of sniffing rate and hippocampal theta rhythm

The coherent episodes between sniffing and theta from baseline recordings (Fig. 9E) were preserved after muscimol injection, although the amplitude and frequency of theta as well as the snif fi ng Fig. 8. Hippocampal fi eld and unit activity relates to sniff cycle. (A) Coronal histological sections from two rats where eight tetrodes were implanted in hippo- campal CA1 region. The black arrow indicates the location of the tetrode tip. (B) Sample recordings of LFP and concurrent snif fi ng (blue) during epochs of high correlation. (C) Frequency histogram of the coherence between sniff and hippocampal LFP. (D) Sample place fi eld maps of CA1 pyramidal neurons from three animals. Left map represents animal trajectory with spikes (red, blue, yellow), whereas on the right is positioned the corresponding fi ring rate map. Bot- tom: spike waveforms of the same place cells. (E) Average polar plots, relative to the sniff cycle for all CA1 place cells (mean SEM) during epochs with no sniff – LFP correlation (left) and during epochs with signi fi cant sniff – LFP correlation (middle). The polar plot on the right represents average burst polarity, rela- tive to sniff cycle, for all CA1 place cells (mean SEM) for the entire recording sessions. (F) Distribution of Z-scores evaluates the significance of phase lock- ing to the sniff cycle of hippocampal place cells for the correlated (red bars) and non-correlated group (blue bars). Signi fi cance probability associated with Z shows the relationship of the neuronal firing frequency across all phase bins (0–360°). Dashed red lines indicate the P = 0.05 significance threshold, and thus all values of Z to the right/left of these lines are signi fi cant at that con fi dence level. (G) Place cell circular statistics: left, average k values for correlated (cor) vs. non-correlated epochs (non-cor); right, average k values for recorded bursts vs. shuf fl ed bursts. (H) Sample 1000-ms autocorrelogram of hippocampal theta- modulated interneuron. (I) Average k values for correlated (cor) vs. non-correlated epochs (non-cor) for interneurons. * P < 0.05. (J) Sample place fi eld maps of CA1 pyramidal neurons from two animals after exploration of rectangular-shaped linear tracks. Left maps represents animal trajectory with spikes (blue, yellow), whereas on the right is the corresponding fi ring rate map. (K) Plot of theta phase (left) and sniff phase (right) vs. time for the overlaid spikes of runs in rectangular-shaped linear tracks for four representative place cells. The values of Pearson ’ s correlation coef fi cient (R 2 ) for each phase correlation are shown
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Input source and strength influences overall firing phase of model hippocampal CA1 pyramidal cells during theta: Relevance to REM sleep reactivation and memory consolidation

Input source and strength influences overall firing phase of model hippocampal CA1 pyramidal cells during theta: Relevance to REM sleep reactivation and memory consolidation

in Hobson and Pace-Schott (2002) and Ribeiro and Nicolelis (2004)). During REM sleep, reactivated fir- ing occurs on a similar timescale as during explora- tion (Louie and Wilson, 2001), and the hippocampal theta rhythm (5–10 Hz), which is critical to learning (Mizumori et al., 1990; Givens, 1996; Rashidy-Pour et al., 1996), resumes or exceeds active waking strength (Vanderwolf et al., 1977). Phase precession of hippocampal place cell firing relative to the theta rhythm also recurs as in waking exploration (Poe et al., 2000; Louie and Wilson, 2001; Harris et al., 2002). As an animal becomes familiar with an envi- ronment over several days, a shift occurs in the overall phase of theta at which cells predominantly fire dur- ing REM reactivation (Poe et al., 2000). In the first 2 days of REM sleep following exploration of an ini- tially novel environment, the majority of spikes oc- curred near the depolarizing peak of the theta rhythm, as during waking. But over the following days as the rat became more familiar with the environment, the mean theta firing phase during REM shifted. By the 5th day, cells fired primarily near the hyperpolarizing trough of the theta cycle. Place cell firing in the hyperpola- rizing theta troughs during REM replay may facilitate depotentiation of synaptic connections involved in place cell ensembles encoding familiar environments to prevent saturation of the network and allow en- coding and storage of new information (Poe et al., 2000).
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Decision time, slow inhibition, and theta rhythm

Decision time, slow inhibition, and theta rhythm

There has been an interest in the relation between brain rhythms (Lindsley, 1952) and reaction time for some time. Lansing (1957) reported that simple reaction time to a flash of light was shorter if the flash was delivered in the positive phase of the occipital alpha waves, and suggested that excitability was higher in this phase. Green and Arduini (1954) reported that hippocampal theta usually occurs together with desynchronized EEG in the neocortex, and hypothesized that the theta is related to arousal. There is still debate as to what functional role is played by the theta rhythm. Some human EEG recording studies have reported that theta phase, rather than amplitude, is correlated with cognitive processes, the so-called phase reset model (Rizzuto et al., 2003; Buzsaki, 2006), whereas other studies on the frontal and temporal lobes have placed more importance on the theta amplitude (Canolty et al., 2006).
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Analysis of Theta Power in Hippocampal EEG During Bar Pressing and Running Behavior in Rats During Distinct Behavioral Contexts

Analysis of Theta Power in Hippocampal EEG During Bar Pressing and Running Behavior in Rats During Distinct Behavioral Contexts

For example, it may be the case that a drop in theta power during consumption is indicative of a state of hypervigilance to any pos- sible sensory input for purposes of detecting nearby predators. This idea of non-theta activity representing a state of hippocampal sen- sitivity to generalized sensory inputs is based on and strongly sup- ported by hippocampal single-cell data from Vinogradova (1995). This framework also broadly fits the theoretical observations of Sainsbury (1998) and Grastyan et al. (1959) that hippocampal theta activity may represent a state of inhibition, not arousal. Be- havioral evidence of such vigilance is directly supported by obser- vations of hyperreactivity to sensory stimuli during atropine infu- sions of the medial septum (Lawson and Bland, 1993), which cause reductions in hippocampal theta activity during immobility. This nonspecific attention could be optimized for use in detecting the approach of predators during consumption of food or water in species such as the rat. Food-rich areas in an actual environment may be more likely to be frequented by predators, especially if the animal is forced to eat outside of its nest, as was the case in this experiment.
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Hippocampal Non-Theta-Contingent Eyeblink Classical Conditioning: A Model System for Neurobiological Dysfunction

Hippocampal Non-Theta-Contingent Eyeblink Classical Conditioning: A Model System for Neurobiological Dysfunction

Joseph J. Cicchese and Stephen D. Berry* Department of Psychology, Center for Neuroscience, Miami University, Oxford, OH, USA Typical information processing is thought to depend on the integrity of neurobiological oscillations that may underlie coordination and timing of cells and assemblies within and between structures. The 3–7 Hz bandwidth of hippocampal theta rhythm is asso- ciated with cognitive processes essential to learning and depends on the integrity of cholinergic, GABAergic, and glutamatergic forebrain systems. Since several significant psychiatric disorders appear to result from dysfunction of medial temporal lobe (MTL) neurochemical systems, preclinical studies on animal models may be an important step in defining and treating such syndromes. Many studies have shown that the amount of hippocampal theta in the rabbit strongly predicts the acquisition rate of classical eyeblink conditioning and that impairment of this system substantially slows the rate of learning and attainment of asymptotic performance. Our lab has developed a brain–computer interface that makes eyeblink training trials contingent upon the explicit presence or absence of hippocampal theta. The behavioral benefit of theta-contingent training has been demonstrated in both delay and trace forms of the paradigm with a two- to fourfold increase in learning speed over non-theta states. The non-theta behavioral impairment is accompanied by disruption of the amplitude and synchrony of hippocampal local field potentials, multiple-unit excitation, and single-unit response patterns dependent on theta state. Our findings indicate a significant electrophysiological and behavioral impact of the pretrial state of the hippocampus that suggests an important role for this MTL sys- tem in associative learning and a significant deleterious impact in the absence of theta. Here, we focus on the impairments in the non-theta state, integrate them into current models of psychiatric disorders, and suggest how improvement in our understanding of neurobiological oscillations is critical for theories and treatment of psychiatric pathology. Keywords: hippocampus, neurobiological oscillations, theta rhythm, brain–computer interface, cognitive dysfunction, psychiatric disorders
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The Dynamics of Networks of Identical Theta Neurons

The Dynamics of Networks of Identical Theta Neurons

Perfect synchrony corresponds to a form of dimension reduction, since the net- work is effectively replaced by a single self-coupled neuron. However, the stability of this state depends on the linearisation of the full dynamics around it. In this paper we use another form of dimension reduction, the Watanabe/Strogatz (WS) ansatz [9, 10], applicable to all-to-all coupled networks of identical phase oscillators. For the ansatz to be applicable, the velocity field of an oscillator has to contain only the first harmonics of the phase variable. The theta neuron [11, 12] is such a model oscillator. The derivation of a network of coupled phase oscillators from a general weakly- coupled network of oscillators is well known [7, 13, 14]. Unlike those derivations, the equation for a theta neuron, involving just one phase variable, is the normal form of a saddle-node-on-a-circle (SNIC) bifurcation, and will thus describe all neurons undergoing this bifurcation, at least in some neighbourhood in a parameter space of the bifurcation. Such a bifurcation leads to the neuron being of Type I [15, 16], i.e. capable of firing at arbitrarily low frequencies.
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Prime Cordial Labeling for Theta Graph

Prime Cordial Labeling for Theta Graph

gcd f u f v and 0 if gcd ( f ( u ), f ( v )) > 1 ; then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1 . A graph which admits a prime cordial labeling is called a prime cordial graph. In this paper, we investigate the prime cordial labeling of Theta graph. We also discuss prime cordial labeling in the context of some graph operations namely duplication, switching, fusion, path union and the graph obtained by joining two copies of Theta graph by a path of arbitrary length . Keywords: Prime cordial labeling, fusion, switching, contraction, path union. AMS Mathematics Subject Classification (2010): 05C78
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A Density Model for a Population of Theta Neurons

A Density Model for a Population of Theta Neurons

In the present study of populations of theta-neurons, we consider only the case with conduction delay. The condition for existence of a global solution (no burst) involves the product of the number of connections J and the maximum of the delay repartition α . In order to satisfy this condition for large J , the delay kernel α should spread over the time interval in order to decrease its maximum. So, it is possible to exhibit populations with the same J that will burst in finite time with the LIF model but will have a regular behavior on an infinite horizon with the QIF model with a different delay repartition.
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On the Lovász theta function and some variants

On the Lovász theta function and some variants

In his seminal paper, Lov´ asz [18] defined the so-called theta function of a graph G, denoted by ϑ(G). He then proved that α(G) ≤ ϑ(G) ≤ χ( ¯ G), where χ( ¯ G) denotes the chromatic number of ¯ G. Gr¨ otschel et al. [12] showed that ϑ(G) can be computed in polynomial time (to arbitrary fixed precision) by solving a semidefinite program (SDP). This result is remarkable, given that computing the chromatic number of a graph, or even approximating it, is also N P -hard in the strong sense (Feige & Killian [8]).

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Hemoglobins in the genome of the cryptomonad Guillardia theta

Hemoglobins in the genome of the cryptomonad Guillardia theta

Endosymbiosis is a fundamental process that has shaped the diversity and evolution of unicellular eukaryotes [1]. “Primary endosymbiosis” - the uptake of a photosyn- thetic cyanobacterium by an early nonphotosynthetic unicellular eukaryote gave rise to the double membrane- bound plastids of glaucophytes, red and green algae, and land plants [1,2]. Subsequent endosymbioses of primary- plastid-containing eukaryotes by nonphotosynthetic hosts, called “secondary endosymbiosis”, gave rise to much of the present day diversity of protists [3]. Although in most protist lineages, reduction of the endosymbiont nucleus has been completed, a remnant nucleus, the nucleomorph is still present in two protist lineages, the cryptomonads and the chloroarachniophytes [4]. The nucleomorphs of these two groups have independent origins: the cryptomo- nad plastid and nucleomorph are of red algal ancestry [5,6] whereas the chlorarachniophyte plastids and nucleo- morphs are of green algal origin [7,8]. Several cryptophyte genomes have been sequenced, including Guillardia theta, Bigelowiella natans, Hemiselmis andersenii and Crypto- monas paramecium [7-10]. Here, we report the presence of hemoglobin genes in the host nuclear genome of G.
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Episodic Memory, Theta-Activity and Schizophrenia

Episodic Memory, Theta-Activity and Schizophrenia

Abstract People with schizophrenia are known to have difficulties with episodic memory (EM). The purpose of this investigation was to examine the relationship between theta-power and: i) behavioural measures of EM performance, ii) event- related potential (ERP) indices of recollection and, iii) measures of schizophrenia symptomatology. In doing so, the aim was to gain a better understanding of the basic neural mechanisms that contribute to successful EM performance, and how these may differ for people with schizophrenia. The present investigation adopted an endophenotypic approach and collected measures of schizotypy from student participants to minimise patient factors that can confound interpretations. Fifty- four participants were asked to complete a reality-monitoring exclusion EM paradigm whilst electroencephalogram (EEG) data were collected. Measures of theta-power and ERPs were time-locked to words presented during the retrieval phase. There was a significant positive correlation between theta-power over Fz between 600-1000ms post-stimulus presentation and estimates of recollection in the imagine condition as well as a significant negative correlation between these measures of theta-power for perceive items and ERP indices of recollection for imagine items. There was also a significant positive correlation between
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Galois action on special theta values

Galois action on special theta values

(where ǫ = 0 for even χ, ǫ = 1 for odd χ) the associated theta series. Its value at its point of symmetry under the modular transformation τ 7→ − 1/τ is related by θ χ (i) = W (χ)θ χ ¯ (i) to the root number of the L-series of χ and hence can be used to calculate the latter quickly if it does not vanish. Using Shimura’s reciprocity law, we calculate the Galois action on these special values of theta functions with odd N normalised by the Dedekind eta function. As a consequence, we prove some experimental results of Cohen and Zagier and we deduce a partial result on the non-vanishing of these special theta values with prime N.
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Congruent number theta coefficients to 10¹²

Congruent number theta coefficients to 10¹²

For a straightforward description of the divide-and-conquer approach to the Chinese Remainder algorithm see [41], pages 57–58. Similar preconditioning and a divide-and-conquer approach can of course be applied to the multimodular reduction phase. A slight adjustment needs to be made to both the reduction and CRT phases to cope with a number of primes which is not a power of 2. An advantage of this multimodular approach to multiplying theta series, which we discuss in more detail below, is that the amount of data written to disk at intermediate stages of the computation can be kept very low, minimising expensive disk read/write operations.
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1 Introduction to Ramanujan theta functions

1 Introduction to Ramanujan theta functions

There is no precise general definition of q-series that I know of. However, it is usually an expression involving the variable q and perhaps other variables in an infinite sum or product. I will give the definition of the most important q-series which is as fundamental to the theory of q-series as the exponential is to differential calculus. Euler applied q-series to the theory of partitions of integers. Later, Jacobi introduced q-series as a basis for his theory of theta and elliptic functions with applications to number theory.

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Some circular summation formulas for theta functions

Some circular summation formulas for theta functions

More recently, Liu further obtained the general formulas for theta functions (see []), but from one main result, Theorem  of Liu, we do not deduce our results in the present paper. Many people research the circular summation formulas of theta functions and find more interesting formulas (see, for details, [–]).

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Mock theta functions and Appell–Lerch sums

Mock theta functions and Appell–Lerch sums

the associated bilateral series of odd order mock theta functions in terms of Appell–Lerch sums. As an application, the associated Ramanujan radial limits of these mock theta func- tions can be constructed as well. Surprisingly, by relating with the new result of Chan and Mao [22], we get a very interesting congruence relationship of the bilateral series B(ω; q) for the third order mock theta function ω(q).

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EARLY DEVELOPMENT OF ALPHA AND THETA BRAINWAVE TRAINING

EARLY DEVELOPMENT OF ALPHA AND THETA BRAINWAVE TRAINING

EEG alpha-theta brainwave neurofeedback therapy (Peniston/Kulkosky protocol) had also been employed in a clinical study using twenty male Vietnam combat veterans with a dual diagnosis of posttraumatic stress disorder and alcohol abuse. A goal of that study was to determine the efficacy of brainwave training in developing brain region synchronization and altering amplitudes of intrasubject brainwaves. It was discovered that during sessions in which patients reported abreactive imagery, the PKBWNT sessions displayed a statistically reliable interaction seen as a "cross-over" pattern in which theta waves gradually increased and the alpha waves decreased. This pattern identifies a state of consciousness which is believed to optimize the surfacing of abreactive images. A follow-up study revealed that only three of the twenty experimental patients had relapsed to alcohol by twenty-six months after PKBWNT (Peniston et al., 1995).
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The theta antigen of mice and its analog in rats

The theta antigen of mice and its analog in rats

Quantitative absorption tests using mouse anti-8 sera and mouse thymocytes as target cells showed that rats of the inbred strains tested all expressed an antigen which was strongly cross[r]

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