Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

Polizeigeschosse und ihre Deformation

In den Jahren 2001 bis 2007 ist bei den Polizeien der deutschen Bundesländer und bei den Polizeikorps der Schweiz die so genannte Polizeimunition eingeführt worden. Von dieser mit einem deformierenden Geschoss ausgerüsteten Munition verspricht man sich eine größere Wirksamkeit und wegen der begrenzten Durchschlagsleistung eine geringere Gefährdung unbeteiligter Personen. Bei geringerer Auftreffenergie deformiert sich jedoch das Geschoss weniger, die Wirksamkeit wird kleiner und die Eindringtiefe größer. In der hier vorgestellten Arbeit wurde die Abhängigkeit der Deformation und der Eindringtiefe in ballistische Seife von der Auftreffenergie für alle 4 gegenwärtig vorhandenen Polizeigeschosse untersucht. Bereits bei Schussdistanzen von 25–30 m ist mit einer verminderten Wirksamkeit zu rechnen. Bei einer viel gebrauchten Waffe kann zudem die Mündungsenergie so stark reduziert sein, dass sich bereits bei kurzen Schussdistanzen die Geschosse nicht mehr erwartungsgemäß deformieren.

A neurophysiological signature of motivational incongruence: EEG changes related to insufficient goal satisfaction

Human behavior and psychological functioning is motivated and guided by individual goals. Motivational incongruence refers to states of insufficient goal satisfaction and is tightly related to psychological problems and even psychopathology. In the present study, individual levels of motivational incongruence were assessed with the incongruence-questionnaire (INC) in a healthy sample. In addition, multi-channel resting-state EEG was measured. Individual variations of EEG synchronization and spectral power were related to individual levels of motivational incongruence. For significant correlations, the relation to intracerebral sources of electrical brain activity was investigated with sLORETA. The results indicate that, even in a healthy sample with rather low degrees of motivational incongruence, this insufficient goal satisfaction is related to consistent changes in resting state brain activity. Upper Alpha band attenuation seems to be most indicative of increased levels of motivational incongruence. This is reflected not only in significantly reduced functional connectivity, but also in changes regarding the level of brain activation, as indicated by significant effects in the spectral power and LORETA analyses. Results are related to research investigating the upper Alpha band and are discussed in the framework of Grawe's consistency theory.

50th anniversary of the Judd–Ofelt theory: An experimentalist's view of the formalism and its application

The theory on the intensities of 4f-4f transitions introduced by B.R. Judd and G.S. Ofelt in 1962 has become a center piece in rare-earth optical spectroscopy over the past five decades. Many fundamental studies have since explored the physical origins of the Judd–Ofelt theory and have proposed numerous extensions to the original model. A great number of studies have applied the Judd–Ofelt theory to a wide range of rare-earth doped materials, many of them with important applications in solid-state lasers, optical amplifiers, phosphors for displays and solid state lighting, upconversion and quantum-cutting materials, and fluorescent markers. This paper takes the view of the experimentalist who is interested in appreciating the basic concepts, implications, assumptions, and limitations of the Judd–Ofelt theory in order to properly apply it to practical problems. We first present the formalism for calculating the wavefunctions of 4f electronic states in a concise form and then show their application to the calculation and fitting of 4f-4f transition intensities. The potential, limitations and pitfalls of the theory are discussed, and a detailed case study of LaCl3:Er3+ is presented.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Microscopic theory of cooperative spin crossover: Interaction of molecular modes with phonons

In this article, we present a new microscopic theoretical approach to the description of spin crossover in molecular crystals. The spin crossover crystals under consideration are composed of molecular fragments formed by the spin-crossover metal ion and its nearest ligand surrounding and exhibiting well defined localized (molecular) vibrations. As distinguished from the previous models of this phenomenon, the developed approach takes into account the interaction of spin-crossover ions not only with the phonons but also a strong coupling of the electronic shells with molecular modes. This leads to an effective coupling of the local modes with phonons which is shown to be responsible for the cooperative spin transition accompanied by the structural reorganization. The transition is characterized by the two order parameters representing the mean values of the products of electronic diagonal matrices and the coordinates of the local modes for the high- and low-spin states of the spin crossover complex. Finally, we demonstrate that the approach provides a reasonable explanation of the observed spin transition in the [Fe(ptz)6](BF4)2 crystal. The theory well reproduces the observed abrupt low-spin → high-spin transition and the temperature dependence of the high-spin fraction in a wide temperature range as well as the pronounced hysteresis loop. At the same time within the limiting approximations adopted in the developed model, the evaluated high-spin fraction vs. T shows that the cooperative spin-lattice transition proves to be incomplete in the sense that the high-spin fraction does not reach its maximum value at high temperature.

Field investigation of dried lakes in western United States as an analogue to desiccation fractures on Mars

Potential Desiccation Polygons (PDPs), tens to hundreds of meters in size, have been observed in numerous regions on Mars, particularly in ancient (>3Gyr old) terrains of inferred paleolacustrine/playa geologic setting, and in association with hydrous minerals such as smectites. Therefore, a better understanding of the conditions in which large desiccation polygons form could yield unique insight into the ancient climate on Mars. Many dried lakebeds/playas in western United States display large (>50m wide) desiccation polygons, which we consider to be analogues for PDPs on Mars. Therefore, we have carried out fieldwork in seven of these dried lakes in San Bernardino and the Death Valley National Park regions complemented with laboratory and spectral analysis of collected samples. Our study shows that the investigated lacustrine/playa sediments have (a) a soil matrix containing 40-75% clays and fine silt (by volume) where the clay minerals are dominated by illite/muscovite followed by smectite, (b) carbonaceous mineralogy with variable amounts of chloride and sulfate salts, and significantly, (c) roughly similar spectral signatures in the visible-near-infrared (VIS-NIR) range. We conclude that the development of large desiccation fractures is consistent with water table retreat. In addition, the comparison of the mineralogical to the spectral observations further suggests that remote sensing VIS-NIR spectroscopy has its limitations for detailed characterization of lacustrine/playa deposits. Finally, our results imply that the widespread distribution of PDPs on Mars indicates global or regional climatic transitions from wet conditions to more arid ones making them important candidate sites for future in situ missions.

On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.