Preconditioning of low-frequency repetitive transcranial magnetic stimulation with transcranial direct current stimulation: evidence for homeostatic plasticity in the human motor cortex

Recent experimental work in animals has emphasized the importance of homeostatic plasticity as a means of stabilizing the properties of neuronal circuits. Here, we report a phenomenon that indicates a homeostatic pattern of cortical plasticity in healthy human subjects. The experiments combined two techniques that can produce long-term effects on the excitability of corticospinal output neurons: transcranial direct current stimulation (TDCS) and repetitive transcranial magnetic stimulation (rTMS) of the left primary motor cortex. "Facilitatory preconditioning" with anodal TDCS caused a subsequent period of 1 Hz rTMS to reduce corticospinal excitability to below baseline levels for >20 min. Conversely, "inhibitory preconditioning" with cathodal TDCS resulted in 1 Hz rTMS increasing corticospinal excitability for at least 20 min. No changes in excitability occurred when 1 Hz rTMS was preceded by sham TDCS. Thus, changing the initial state of the motor cortex by a period of DC polarization reversed the conditioning effects of 1 Hz rTMS. These preconditioning effects of TDCS suggest the existence of a homeostatic mechanism in the human motor cortex that stabilizes corticospinal excitability within a physiologically useful range

Abelian Functions for Cyclic Trigonal Curves of Genus Four

We discuss the theory of generalized Weierstrass $\sigma$ and $\wp$ functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve $y^3=x^5+\lambda_4 x^4 +\lambda_3 x^3+\lambda_2 x^2 +\lambda_1 x+\lambda_0$ is discussed in detail, including a list of some of the associated partial differential equations satisfied by the $\wp$ functions, and the derivation of an addition formulae.Comment: 23 page

Study of polarization observables in double pion photoproduction on the proton

Using a model for two pion photoproduction on the proton previously tested in total cross sections and invariant mass distributions, we evaluate here polarization observables on which recent experiments are providing new information. We evaluate cross sections for spin 1/2 and 3/2, which are measured at Mainz and play an important role in tests of the GHD sum rule. We also evaluate the proton polarization asymmetry $\Sigma$ which is currently under investigation at GRAAL in Grenoble.Comment: 23 pages, 14 ps figure

Localization and Causality for a free particle

Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle described by either the Dirac equation or the Klein-Gordon equation because such a particle cannot be localized in the sense required by the theorems.Comment: 9 pages,no figures,new section adde

Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

Generalised Elliptic Functions

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed sees the functions defined as logarithmic derivatives of the sigma-function, a modified Riemann theta-function. We can make use of known properties of the sigma function to derive power series expansions and in turn the properties mentioned above. This approach has been extended to a wide range of non hyperelliptic and higher genus curves and an overview of recent results is given. The second approach defines the functions algebraically, after first modifying the curve into its equivariant form. This approach allows the use of representation theory to derive a range of results at lower computational cost. We discuss the development of this theory for hyperelliptic curves and how it may be extended in the future.Comment: 16 page

Electron self-trapping in intermediate-valent SmB6

SmB6 exhibits intermediate valence in the ground state and unusual behaviour at low temperatures. The resistivity and the Hall effect cannot be explained either by conventional sf-hybridization or by hopping transport in an impurity band. At least three different energy scales determine three temperature regimes of electron transport in this system. We consider the ground state properties, the soft valence fluctuations and the spectrum of band carriers in n-doped SmB6. The behaviour of excess conduction electrons in the presence of soft valence fluctuations and the origin of the three energy scales in the spectrum of elementary excitations is discussed. The carriers which determine the low-temperature transport in this system are self-trapped electron-polaron complexes rather than simply electrons in an impurity band. The mechanism of electron trapping is the interaction with soft valence fluctuations.Comment: 12 pages, 3 figure

Levodopa-induced dyskinesia in Parkinson&apos;s disease: sleep matters

OBJECTIVE: The spectrum of clinical symptoms changes during the course of Parkinson's disease. Levodopa therapy, while offering remarkable control of classical motor symptoms, causes abnormal involuntary movements as the disease progresses. These levodopa-induced dyskinesias (LIDs) have been associated with abnormal cortical plasticity. Since slow wave activity (SWA) of nonrapid eye movement (NREM) sleep underlies adjustment of cortical excitability, we sought to elucidate the relationship between this physiological process and LIDs. METHODS: Thirty-six patients at different stages of Parkinson's disease (PD) underwent whole-night video polysomnography-high-density EEG (vPSG-hdEEG), preceded by 1 week of actigraphy. To represent the broad spectrum of the disease, patients were divided into three groups by disease stage, (i) de novo (DNV; n = 9), (ii) advanced (ADV; n = 13), and (iii) dyskinetic (DYS; n = 14) and were compared to an age-matched control group (CTL; n = 12). The SWA-NREM content of the PSG-hdEEG was then temporally divided into 10 equal parts, from T1 to T10, and power and source analyses were performed. T2-T3-T4 were considered early sleep and were compared to T7-T8-T9, representing late sleep. RESULTS: We found that all groups, except the DYS group, manifested a clear-cut SWA decrease between early and late sleep. INTERPRETATION: Our data demonstrate a strong pathophysiological association between sleep and PD. Given that SWA may be a surrogate for synaptic strength, our data suggest that DYS patients do not have adequate synaptic downscaling. Further analysis is needed to determine the effect of drugs that can enhance cortical SWA in LIDs

Calculation of Effective Coulomb Interaction for Pr3+Pr^{3+}, U4+U^{4+}, and UPt3UPt_3

In this paper, the Slater integrals for a screened Coulomb interaction of the the Yukawa form are calculated and by fitting the Thomas-Fermi wavevector, good agreement is obtained with experiment for the multiplet spectra of $Pr^{3+}$ and $U^{4+}$ ions. Moreover, a predicted multiplet spectrum for the heavy fermion superconductor $UPt_3$ is shown with a calculated Coulomb U of 1.6 eV. These effective Coulomb interactions, which are quite simple to calculate, should be useful inputs to further many-body calculations in correlated electron metals.Comment: 8 pages, revtex, 3 uuencoded postscript figure