Theta Group Research Articles

Exploring trait differences in neurofeedback learners: a single-session sham-controlled pilot study

AbstractNeurofeedback (NF) is a form of biofeedback that involves individuals monitoring and shifting brain activity towards a desired direction. The objective of this study was to investigate whether there are differences between NF learners and non-learners on psychometric traits such as the NEO PI-R personality factors, self-regulation questionnaire (SRQ) and the need for cognition scale (NFC). A total of 34 participants were randomly allocated to a single-blind randomised sham-controlled protocol 3-arm study of single-session theta NF. Twelve participants were administered a spatially defined frontal-midline theta (FM-theta) group, 11 to a functionally defined medial temporal/parietal lobe (MTL-theta) group and 11 allocated to a yoked sham NF group. The baseline session included screening of participants, trait-based behavioural measures (SRQ, NFC and NEO PI-R) and the completion of cognitive tasks with electroencephalography (EEG) recording to determine individualised peak theta activity for NF training. NF learners and non-learners were evaluated using changes in absolute theta power and the percentage of time spent above threshold using Spearman’s correlation coefficient from a total of 30-minutes of NF exposure. Significant differences in psychometric traits between NF learners and non-learners differed depending on learning metrics. Results indicated that NF learners reported higher SRQ total scores, SRQ decision making, SRQ goal setting subfactors and NEO PI-R conscientiousness, but were significantly lower in NEO PI-R extraversion compared to non-learners. This study demonstrates that learning outcomes vary based on the metrics used and emphasises the importance of selecting appropriate learning metrics and further examination of learning within sham NF training.

Individual differences in late positive potential amplitude and theta power predict cue-induced eating

Cue-induced reward-seeking behaviors are regulated by both the affective and cognitive control systems of the brain. This study aimed at investigating how individual differences in affective and cognitive responses to cues predicting food rewards contribute to the regulation of cue-induced eating. We recorded electroencephalogram (EEG) from 59 adults while they viewed emotional and food-related images that preceded the delivery of food rewards (candies) or non-food objects (beads). We measured the amplitude of the late positive potential (LPP) in response to a variety of motivationally relevant images and power in the theta (4-8 Hz) frequency band after candies or beads were dispensed to the participants. We found that individuals with larger LPP responses to food images than to pleasant images (C>P group) ate significantly more during the experiment than those with the opposite response pattern (P>C group, p < 0.001). Furthermore, we found that individuals with higher theta power after dispensation of the candy than of the bead (θCA>θBE) ate significantly more than those with the opposite response pattern (θBE>θCA, p < 0.001). Finally, we found that the crossed P>C and θBE>θCA group ate less (p < 0.001) than did the other three groups formed by crossing the LPP and theta group assignments, who exhibited similar eating behavior on average (p = 0.662). These findings demonstrate that individual differences in both affective and cognitive responses to reward-related cues underlie vulnerability to cue-induced behaviors, underscoring the need for individualized treatments to mitigate maladaptive behaviors.

Comparison the accuracy of a novel implant robot surgery and dynamic navigation system in dental implant surgery: an in vitro pilot study

BackgroundTo compare the accuracy of dental implant placement using a novel dental implant robotic system (THETA) and a dynamic navigation system (Yizhimei) by a vitro model experiment.Methods10 partially edentulous jaws models were included in this study, and 20 sites were randomly assigned into two groups: the dental implant robotic system (THETA) group and a dynamic navigation system (Yizhimei) group. 20 implants were placed in the defects according to each manufacturer’s protocol respectively. The implant platform, apex and angle deviations were measured by fusion of the preoperative design and the actual postoperative cone-beam computed tomography (CBCT) using 3D Slicer software. Data were analyzed by t - test and Mann-Whitney U test, p < 0.05 was considered statistically significant.ResultsA total of 20 implants were placed in 10 phantoms. The comparison deviation of implant platform, apex and angulation in THETA group were 0.58 ± 0.31 mm, 0.69 ± 0.28 mm, and 1.08 ± 0.66° respectively, while in Yizhimei group, the comparison deviation of implant platform, apex and angulation were 0.73 ± 0.20 mm, 0.86 ± 0.33 mm, and 2.32 ± 0.71° respectively. The angulation deviation in THETA group was significantly smaller than the Yizhimei group, and there was no significant difference in the deviation of the platform and apex of the implants placed using THETA and Yizhimei, respectively.ConclusionThe implant positioning accuracy of the robotic system, especially the angular deviation was superior to that of the dynamic navigation system, suggesting that the THETA robotic system could be a promising tool in dental implant surgery in the future. Further clinical studies are needed to evaluate the current results.

Fourier Interpolation with Zeros of Zeta and L-Functions

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other L-functions. We establish a duality principle for Fourier interpolation bases in terms of certain kernels of general Dirichlet series with variable coefficients. Such kernels admit meromorphic continuation, with poles at a sequence dual to the sequence of frequencies of the Dirichlet series, and they satisfy a functional equation. Our construction of concrete bases relies on a strengthening of Knopp’s abundance principle for Dirichlet series with functional equations and a careful analysis of the associated Dirichlet series kernel, with coefficients arising from certain modular integrals for the theta group.

The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3

We show that the average size of the $2$-Selmer group of the family of Jacobians of non-hyperelliptic genus-$3$ curves with a marked rational hyperflex point, when ordered by a natural height, is bounded above by $3$. We achieve this by interpreting $2$-Selmer elements as integral orbits of a representation associated with a stable $\mathbb{Z}/2\mathbb{Z}$-grading on the Lie algebra of type $E_6$ and using Bhargava's orbit-counting techniques. We use this result to show that the marked point is the only rational point for a positive proportion of curves in this family. The main novelties are the construction of integral representatives using certain properties of the compactified Jacobian of the simple curve singularity of type $E_6$, and a representation-theoretic interpretation of a Mumford theta group naturally associated to our family of curves.

Individual differences in neuroanatomy and neurophysiology predict effects of transcranial alternating current stimulation

BackgroundNoninvasive transcranial electrical stimulation (tES) research has been plagued with inconsistent effects. Recent work has suggested neuroanatomical and neurophysiological variability may alter tES efficacy. However, direct evidence is limited. ObjectiveWe have previously replicated effects of transcranial alternating current stimulation (tACS) on improving multitasking ability in young adults. Here, we attempt to assess whether these stimulation parameters have comparable effects in older adults (aged 60–80 years), which is a population known to have greater variability in neuroanatomy and neurophysiology. It is hypothesized that this variability in neuroanatomy and neurophysiology will be predictive of tACS efficacy. MethodsWe conducted a pre-registered study where tACS was applied above the prefrontal cortex (between electrodes F3-F4) while participants were engaged in multitasking. Participants were randomized to receive either 6-Hz (theta) tACS for 26.67 min daily for three days (80 min total; Long Exposure Theta group), 6-Hz tACS for 5.33 min daily (16-min total; Short Exposure Theta group), or 1-Hz tACS for 26.67 min (80 min total; Control group). To account for neuroanatomy, magnetic resonance imaging data was used to form individualized models of the tACS-induced electric field (EF) within the brain. To account for neurophysiology, electroencephalography data was used to identify individual peak theta frequency. ResultsResults indicated that only in the Long Theta group, performance change was correlated with modeled EF and peak theta frequency. Together, modeled EF and peak theta frequency accounted for 54%–65% of the variance in tACS-related performance improvements, which sustained for a month. ConclusionThese results demonstrate the importance of individual differences in neuroanatomy and neurophysiology in tACS research and help account for inconsistent effects across studies.

The Effects of Theta EEG Neurofeedback on the Consolidation of Spatial Memory.

How can the stability of a recently acquired memory be improved? Recent findings regarding the importance of theta frequency EEG activity in the hippocampus suggest that entraining neural activity in that frequency band might increase post-encoding waking replay, reinforcing learning-related plasticity. Our previous studies revealed that upregulating postlearning theta power using EEG neurofeedback (NFB) significantly benefitted procedural and episodic memory performance (both immediate and delayed), and may provide optimal conditions for stabilization of new memories. We have now explored whether memory benefits of theta NFB generalize to delayed spatial memory, an additional hippocampus-dependent process. Participants learned to associate object images with locations on a computer screen. NFB was used to enable participants to selectively increase scalp EEG theta power for 30 minutes. Visuo-spatial memory was tested one week later, with the theta NFB participants compared with 2 control groups (beta-augmentation NFB as an active control group, and an additional passive control group that did not engage in NFB). Theta upregulation was found to improve visuo-spatial memory, as reflected in reduced error distances in location marking and faster reaction time for correct answers by the theta group. This supports the contention that theta upregulation immediately after learning strengthens early consolidation of visuo-spatial memory. This intervention could potentially benefit various memory-challenged populations, as well as healthy individuals.

Theta EEG neurofeedback benefits early consolidation of motor sequence learning.

Procedural learning is subject to consolidation processes believed to depend on the modulation of functional connections involved in representing the acquired skill. While sleep provides the most commonly studied framework for such consolidation processes, posttraining modulation of oscillatory brain activity may also impact on plasticity processes. Under the hypothesis that consolidation of motor learning is associated with theta band activity, we used EEG neurofeedback (NFB) to enable participants to selectively increase either theta or beta power in their EEG spectra following the acquisition phase of motor sequence learning. We tested performance on a motor task before and after training, right after the NFB session to assess immediate NFB effects, 1 day after NFB to assess interaction between NFB effects and overnight sleep-dependent stabilization, and 1 week after the initial session, to assess the effects of NFB on long-term stabilization of motor training. We also explored the extent of the influence of single-electrode NFB on EEG recorded across the scalp. Results revealed a significantly greater improvement in performance immediately after NFB in the theta group than in the beta group. This effect continued for testing up to 1 week following training. Across participants, post-NFB improvement correlated positively with theta/beta ratio change achieved during NFB. Additionally, NFB was found to cause widespread band-power modulation beyond the electrode used for feedback. Thus, upregulating postlearning theta power may yield contributions to the immediate performance and subsequent consolidation of an acquired motor skill.

Dirichlet series with functional equations and arithmetical identities

Exploiting the functional equation of Hecke-type associated with a function satisfying a modular relation with a residual function as developed in Bochner (J Indian Math Soc 16:99–102, 1952), Chandrasekharan and Narasimhan (Ann Math 74:1–23, 1961) derived the equivalence of the functional equation to two arithmetical identities. Hawkins and Knopp (Contemp Math 143:451–475, 1993) showed the equivalence of the functional equation to modular integrals with rational period functions of weight 2k, \(k \in \mathbb {Z}^+\) on the theta group \(\Gamma _\vartheta \). The aim of the current work is to show that results analogous to those of Chandrasekharan and Narasimhan can be developed in the Hawkins and Knopp context, but with respect to the full modular group \(\Gamma (1)\), rather than the theta group \(\Gamma _\vartheta \).

Better than sleep: Theta neurofeedback training accelerates memory consolidation

Consistent empirical results showed that both night and day sleep enhanced memory consolidation. In this study we explore processes of consolidation of memory during awake hours. Since theta oscillations have been shown to play a central role in exchange of information, we hypothesized that elevated theta during awake hours will enhance memory consolidation.We used a neurofeedback protocol, to enhance the relative power of theta or beta oscillations. Participants trained on a tapping task, were divided into three groups: neurofeedback theta; neurofeedback beta; control. We found a significant improvement in performance in the theta group, relative to the beta and control groups, immediately after neurofeedback. Performance was further improved after night sleep in all groups, with a significant advantage favoring the theta group. Theta power during training was correlated with the level of improvement, indicating a clear relationship between memory consolidation, and theta neurofeedback.

Excess beta activity in the EEG of children with attention-deficit/hyperactivity disorder: A disorder of arousal?

Past research has reported that a small proportion of children with attention-deficit/hyperactivity disorder (AD/HD) have excess beta activity in their EEG, rather than the excess theta typical of the syndrome. This atypical group has been tentatively labeled as hyperaroused. The aim of this study was to determine whether these children have a hyperaroused central nervous system. Participants included 104 boys aged 8 to 13years old, with a diagnosis of either the Combined or Inattentive type of AD/HD (67 combined type), and 67 age-matched male controls. Ten and a half minutes of EEG and skin conductance (SCL) were simultaneously recorded during an eyes-closed resting condition. The EEG was Fourier transformed and estimates of total power, and relative power in the delta, theta, alpha, and beta bands, and the theta/beta ratio, were calculated. AD/HD patients were divided into an excess beta group and a typical excess theta group. Relative to controls, the typical excess theta group had significantly increased frontal total power, theta and theta/beta ratio, with reduced alpha and beta across the scalp. The excess beta group had significantly reduced posterior total power, increased centro-posterior delta, globally reduced alpha, globally increased beta activity, and globally reduced theta/beta ratio. Both AD/HD groups had significantly reduced SCL compared to the control group, but the two groups did not differ from each other on SCL. These results indicate that AD/HD children with excess beta activity are not hyperaroused, and confirm that the theta/beta ratio is not associated with arousal. This is the first study of arousal measures in AD/HD children with excess beta activity, and has implications for existing models of AD/HD.

Equivariant gerbes on complex tori

We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line bundles. The theta group of symmetries of the gerbe has the structure of a Picard groupoid. We calculate it explicitly as a central extension of the group of symmetries of the gerbe by the Picard groupoid of the underlying complex torus. We discuss obstruction to equivariance and give an example of a group of symmetries of a gerbe with respect to which the gerbe cannot be equivariant. We calculate the obstructions to invariant gerbes for some group of translations of a torus to be equivariant. We survey various types of representations of the group of symmetries of a gerbe on the stack of sheaves of modules on the gerbe and the associated abelian category of sheaves on the gerbe (twisted sheaves).

THE CHIRAL SUPERSTRING SIEGEL FORM IN DEGREE TWO IS A LIFT

We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t=2 over the theta group 1(1 ; 2) to Siegel modular cusp forms over certain subgroups para ( t; 1 ; 2) of paramodular groups. The theta group lift given here is a modication of the Gritsenko lift.

Computing modular correspondences for abelian varieties

In this paper, we describe an algorithm to compute modular correspondences in the coordinate system provided by the theta null points of abelian varieties together with a theta structure. As an application, this algorithm can be used to speed up the initialization phase of a point counting algorithm (Carls and Lubicz, 2008 [CL08]). The main part of the algorithm is the resolution of an algebraic system for which we have designed a specialized Gröbner basis algorithm. Our algorithm takes advantage of the structure of the algebraic system in order to speed up the resolution. We remark that this special structure comes from the action of the automorphisms of the theta group on the solutions of the system which has a nice geometric interpretation. In particular we were able to count the solutions of the system and to identify which ones correspond to valid theta null points.

Epoetin Theta with a New Dosing Schedule in Anaemic Cancer Patients Receiving Nonplatinum-Based Chemotherapy: A Randomised Controlled Trial

IntroductionRecombinant human erythropoietin (r-HuEPO) is used to treat symptomatic anaemia due to chemotherapy. A new r-HuEPO, Epoetin theta (Eporatio®), was investigated and compared to placebo in a randomised, double-blind clinical trial in adult cancer patients receiving nonplatinum-based chemotherapy. The primary efficacy endpoint was the responder rate (complete haemoglobin (Hb) response, i.e., Hb increase ≥2 g/dl) without the benefit of a transfusion within the previous 4 weeks.Research Design and Methods186 patients were randomised to s.c. treatment for 12 weeks with either Epoetin theta (N = 95) or placebo (N = 91). The starting dose was 20,000 IU once weekly Epoetin theta or placebo.ResultsThe incidence of complete Hb responders was significantly higher in the Epoetin theta group than in the placebo group (72.6 vs. 25.3%, P < 0.0001). More patients in the placebo group than in the Epoetin theta group received blood transfusions after randomisation (23 patients, 25.3% vs. 13 patients, 13.7%, P = 0.0277). The majority of patients with a complete Hb response had 20,000 IU/week as their maximum dose prior to response, indicating that a dose of 20,000 IU is an appropriate starting dose. The overall frequencies of adverse events (AEs) were similar in both treatment groups. Hypertension was the only AE that was more frequent in the Epoetin theta group compared to the placebo group (8.4 vs. 1.1%).ConclusionsEpoetin theta showed a superior efficacy to placebo in terms of complete Hb response without blood transfusion within the previous 4 weeks. Treatment with Epoetin theta resulted in a statistically significant increase in mean haemoglobin levels compared to placebo. The overall frequencies of adverse events were similar in both treatment groups.

Binary forms and the hyperelliptic superstring Ansatz

We give a hyperelliptic formulation of the Ansatz of D’Hoker and Phong. We give an explicit family of binary invariants, one for each genus, that satisfies this hyperelliptic Ansatz. We also prove that this is the unique family of weight eight binary forms over the theta group on the hyperelliptic locus that satisfies this Ansatz. Furthermore, we prove that this solution may also be obtained by applying Thomae’s map to multivalued Siegel modular forms of Grushevsky and making certain choices of roots.

Epoetin Theta in Anaemic Cancer Patients Receiving Platinum‐Based Chemotherapy: A Randomised Controlled Trial

IntroductionRecombinant human erythropoietin (r-HuEPO) is used to treat symptomatic anaemia due to chemotherapy. A new r-HuEPO, Epoetin theta (Eporatio®), was investigated and compared to placebo and Epoetin beta in a randomised, double-blind clinical trial in adult cancer patients receiving platinum-based chemotherapy, using a fixed weekly starting dose of 20,000 IU Epoetin theta. The primary efficacy endpoint was the responder rate (complete Hb response, Hb increase ≥ 2 g/dL).Research Design and Methods223 patients were randomised to s.c. treatment for 12 weeks with either Epoetin theta (n = 76) once per week, Epoetin beta (n = 73) three times per week or placebo (n = 74). The starting dose was 20,000 IU once weekly Epoetin theta or 450 IU/kgBW per week Epoetin beta administered in 3 equal weekly doses.ResultsIn the Epoetin theta group were significantly more responders than in the placebo group (65.8 vs. 20.3%, P < 0.0001). Epoetin beta was also more effective than placebo (71.2 vs. 20.3%, P < 0.0001). The mean weekly dose at the time of complete Hb response was lower in the Epoetin theta group (30,000 IU) than in the Epoetin beta group (42,230 IU). Epoetin theta was clearly more effective than placebo.ConclusionThis small study showed, that Epoetin theta is a safe and effective treatment of symptomatic anaemia due to platinum-based chemotherapy in cancer patients.

A note on the Verlinde bundles on elliptic curves

We study the splitting properties of the Verlinde bundles over elliptic curves. Our methods rely on the explicit description of the moduli space of semistable vector bundles on elliptic curves, and on the analysis of the symmetric powers of the Schrodinger representation of the Theta group.

Renewal-type limit theorem for continued fractions with even partial quotients

AbstractWe prove the existence of the limiting distribution for the sequence of denominators generated by continued fraction expansions with even partial quotients, which were introduced by Schweiger [Continued fractions with odd and even partial quotients. Arbeitsberichte Math. Institut Universtät Salzburg4 (1982), 59–70; On the approximation by continues fractions with odd and even partial quotients. Arbeitsberichte Math. Institut Universtät Salzburg1–2 (1984), 105–114] and studied also by Kraaikamp and Lopes [The theta group and the continued fraction expansion with even partial quotients. Geom. Dedicata59(3) (1996), 293–333]. Our main result is proven following the strategy used by Sinai and Ulcigrai [Renewal-type limit theorem for the Gauss map and continued fractions. Ergod. Th. &amp; Dynam. Sys.28 (2008), 643–655] in their proof of a similar renewal-type theorem for Euclidean continued fraction expansions and the Gauss map. The main steps in our proof are the construction of a natural extension of a Gauss-like map and the proof of mixing of a related special flow.

Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the $n$-Dimensional Hyperbolic Space

This paper deals with a new analytic type of vector- and Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups Eisenstein- and Poincaré type series that are annihilated by Dirac operators, and more generally, by iterated Dirac operators on the upper half-space of $\mathbb{R}^n$ are discussed. In particular we introduce (poly-)monogenic modular forms on hypercomplex generalizations of the classical theta group.