Can MRI Contribute to the Understanding and Therapy of Mental Diseases?

The nowadays most accepted hypothesis of the origin of mental diseases is an impaired connectivity between various brain areas. Magnetic resonance tractography reveals structural connectivities through neuronal fibers and resting state functional imaging allows one to visualize functional connectivities. The detection of the small signal changes needs the highest sensitivity and the magnetic resonance imaging scans must be repeated as fast as possible. Statistical evaluation and cross correlation of the signals in all voxels show synchrony of signal-level fluctuations even in remote brain areas. This makes it possible to establish brain networks. The most important of them are the default mode network, the salience network, and the central executive network. Applications to schizophrenia and depression will be discussed. In deep brain stimulation, the excitation, currently used for therapy of Parkinson’s disease, is now introduced for therapy of major depressive disorder and can be taylored to the necessary brain location.     

Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing “jumpy” transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e.g. high level of corruption) to a desirable one (low level of corruption).     

Simultaneous velocity and temperature measurements in gaseous flow fields using the VENOM technique

We present an initial demonstration of simultaneous velocity and temperature mapping in gaseous flow fields using a new nitric oxide planar laser-induced fluorescence-based method. The vibrationally excited NO monitoring (VENOM) technique is an extension of two-component velocimetry using vibrationally excited NO generated from the photodissociation of seeded NO(2) [Appl. Opt. 48, 4414 (2009)], where the two sequential fluorescence images are obtained probing two different rotational states to provide both velocity and temperature maps. Comparisons to computational fluid dynamics simulations show that the initial VENOM measurements provide good velocity and temperature maps in the relatively high-density regions of the flow, where the rms uncertainties are approximately 5% for velocity and 9% for temperature.     

Profile structures of TJ-II stellarator plasmas

Fine structures are found in the TJ-II stellarator electron temperature and density profiles, when they are measured using a high spatial resolution Thomson scattering system. These structures consist of peaks and valleys superimposed to a smooth average. Some irregularities remain in an ensemble average of discharges with similar macroscopic parameters such as line density, central temperature, and plasma current. They are found in all the magnetic configurations explored in plasmas heated by electron cyclotron waves. Their characteristics are shown and their possible origin is discussed.     

On the existence of matrices with constrained elements,rows and columns

Let the following be given: two n × m real matrices, E and F, such that F ? E, three real n-rows, p, a and b, such that b ? a, and three real m-columns, t, c and d, such that d ? c. We give inequalities relating the given matrices and vectors, equivalent to the consistency of the system

$\text{F ? X ? E}$

,

$\text{d ? Xt ? c}$

,

$\text{b ? pX ?a}$

, where X is an n × m unknown real matrix.     

Laser-particulate interactions in a dusty RF plasma

The interaction of particulates formed in an argon RF discharge containing 1-5% CCl₂F₂ admixture with a pulsed infrared laser (Nd:YAG, intensity ~10⁹ W m^-2, pulse duration ~10^-4 s) has been studied in situ. The white light emitted during this process has been monitored as a function of time and wavelength using a fast photo diode and an optical multichannel analyser. The spectra have been fitted with blackbody curves with a standard deviation of 5%. A spectral temperature of about 3500 K has been obtained for various plasma conditions and attributed to the decomposition temperature of the particulate material. A model based on laser heating, internal heat conduction and chemical decomposition is compared with the experimental results. This model predicts the time constants for heating and decomposition of the particulates and explains the dependence of the measured emission intensity on the laser intensity     

The Wigner function for two dimensional tori: Uniform approximation and projections

The Wigner representation of a quantum state, corresponding to a classically integrable Hamiltonian, has been shown to be intimately tied to a classical phase space torus of the same energy. The fact that the semiclassical approximation of the Wigner function there derived turns out to be singular on the torus, as well as on the “Wigner caustic” which contains it, is due to well known limitations of the stationary phase method. The uniform approximation, here derived, does indeed ascribe to the Wigner function a high amplitude along the Wigner caustic, but this is modulated by rapid oscillations except at the torus itself. Asymptotic expansion away from the torus leads back to the semiclassical approximation. Close to the torus the Wigner function is described by a simple transitional approximation which can be resolved into a product of Wigner functions corresponding to one dimensional tori. These results permit one to explicitly project the Wigner function onto any (Lagrangian) coordinate plane so as to obtain the corresponding wave intensity.     

Shifted identical bands: A new phenomenon

The levels in ¹⁶²Gd were identified in spontaneous fission studies. Its transition energies are remarkably similar to those in ¹⁶⁰Gd. From that work, an analysis of yrast bands in even-even proton to neutron-rich Ba to Pb nuclei led to the discovery of a new phenomenon, shifted identical bands (SIB). SIBs are yrast bands in neighboring nuclei (a, b) with moments of inertia which are identical when shifted by a constant amount κ, so J _1a (1+κ)=J _1b , from 2⁺ to 8⁺ and higher to 16⁺. Out of over 700 comparisons, 55 SIBs were found from stable to the most neutron-rich Ce-W nuclei with $\left| {\bar k} \right|$ between 1.5% and 13%, where the spread in κ is less than ±1%, and only four identical bands ( $\bar k \cong 0$ ). As examples, we found for ¹⁵⁸Sm-¹⁶⁰Gd, $\bar k = \left( { - 3.2_{ - 0.2}^{ + 0.1} } \right)\%$ (where the ± is the total spread in κ from ?3.1 to ?3.4); ¹⁵⁶Nd-¹⁶⁰Gd, (?10.6 _?0.2 ^+0.4 )%; ¹⁵⁸Sm-¹⁶⁰Sm, (3.4 _?0.3 ^+0.5 )%. The J ₁ values were fitted to a variable moment of inertia model with parameters J ₀ and C whose values correlate with the SIB J ₁ values. The SIBs are not correlated either with deformation or with the N _p N _n product of the IBA model.     

The Construction of Frobenius Manifolds¶from KP tau-Functions

Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function. Received: 1 September 1998 / Accepted: 7 March 1999     

LM-g splines

As an extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types I, II, and III are introduced. Each is defined in terms of two differential operators the coefficients a_j, J = 0,…, n − 1, and b_i, I = 0,…, m, are sufficiently smooth; and b_m is bounded away from zero on [0, T]. Each of the above types of splines is the solution of an optimization problem more general than the one used in the definition of the L-g spline and hence it is recognized as an entity which is distinct from and more general mathematically than the L-g spline. The LM-g splines introduced here reduce to an L-g spline in the special case in which m = 0 and b₀ = constant ≠ 0. After the existence and uniqueness conditions, characterization, and best approximation properties for the proposed splines are obtained in an appropriate reproducing kernel Hilbert space framework, their usefulness in extending the range of applicability of spline theory to problems in estimation, optimal control, and digital signal processing are indicated. Also, as an extension of recent results in the generalized spline literature, state variable models for the LM-g splines introduced here are exhibited, based on which existing least squares algorithms can be used for the recursive calculation of these splines from the data.