Partial information decomposition as a unified approach to the specification of neural goal functions

In many neural systems anatomical motifs are present repeatedly, but despite their structural similarity they can serve very different tasks. A prime example for such a motif is the canonical microcircuit of six-layered neo-cortex, which is repeated across cortical areas, and is involved in a number of different tasks (e.g. sensory, cognitive, or motor tasks). This observation has spawned interest in finding a common underlying principle, a ‘goal function’, of information processing implemented in this structure. By definition such a goal function, if universal, cannot be cast in processing-domain specific language (e.g. ‘edge filtering’, ‘working memory’). Thus, to formulate such a principle, we have to use a domain-independent framework. Information theory offers such a framework. However, while the classical framework of information theory focuses on the relation between one input and one output (Shannon’s mutual information), we argue that neural information processing crucially depends on the combination of multiple inputs to create the output of a processor. To account for this, we use a very recent extension of Shannon Information theory, called partial information decomposition (PID). PID allows to quantify the information that several inputs provide individually (unique information), redundantly (shared information) or only jointly (synergistic information) about the output. First, we review the framework of PID. Then we apply it to reevaluate and analyze several earlier proposals of information theoretic neural goal functions (predictive coding, infomax and coherent infomax, efficient coding). We find that PID allows to compare these goal functions in a common framework, and also provides a versatile approach to design new goal functions from first principles. Building on this, we design and analyze a novel goal function, called ‘coding with synergy’, which builds on combining external input and prior knowledge in a synergistic manner. We suggest that this novel goal function may be highly useful in neural information processing

Numerical methods for the TSD equation in conservation law form

The Transonic Small Disturbance (TSD) Equation is a common model equation for describing subsonic and supersonic flow close to the local speed of sound (transonic). In transonic flow there is an embedded region of locally supersonic flow inside an otherwise subsonic flow. The supersonic region is usually terminated by a shock discontinuity. The success of a numerical scheme for transonic flow prediction depends on its capability of capturing all the flow details and non-linearities including sharp shock profiles without oscillations near the shock. Most of the important phenomena in the TSD equation occur in the stream-wise direction. The nonlinearity and changes in the region of influence depend only on the stream-wise derivation. A suitable one-dimensional model equation derived from the TSD Equation is used. The one-dimensional equation is written in conservation law form. This nonlinear system of equations models the transition from supersonic to subsonic flow. In the numerical calculations the discretised problem is treated as a series of Riemann problems. We will investigate various techniques for solving these Riemann problems. It will be shown that the techniques do not allow non-physical expansion shocks to develop and that the techniques smooth out expansion shocks when these non-physical shocks are present in the initial velocity profile. A comparison will be made between the schemes based on the sharpness of the resulting shock profiles

Strain dependence of the acoustic properties of amorphous metals below 1K: Evidence for the interaction between tunneling states

We have conducted a thorough study of the acoustic properties between 10^-4 and 1 Kelvin for the amorphous metal Zr_x Cu_1-x (x=0.3 and x=0.4), by measuring the relative change of sound velocity dv/v and internal friction Q^-1 as a function of temperature and also of the applied strain, in both superconducting and normal state. We have found that when plotted versus the ratio of strain energy to thermal energy, all measurements display the same behavior: a crossover from a linear regime of ``independent'' tunneling systems at very low strains and/or high enough temperatures to a nonlinear regime where dv/v and Q^-1 depend on applied strain and the tunneling systems cannot be considered as independent.Comment: 4 pages, 4 figures (submitted to PRL

Regulation of the interplanetary magnetic flux

In this study we use a recently developed technique for measuring the 2-D magnetic flux in the ecliptic plane to examine (1) the long term variation of the magnetic flux in interplanetary space and (2) the apparent rate at which coronal mass ejections (CMEs) may be opening new flux from the Sun. Since there is a substantial variation ({approximately}50%) of the flux in the ecliptic plane over the solar cycle, we conclude that there must be some means whereby new flux can be opened from the Sun and previously open magnetic flux can be closed off. We briefly describe recently discovered coronal disconnections events which could serve to close off previously open magnetic flux. CMEs appear to retain at least partial magnetic connection to the Sun and hence open new flux, while disconnections appear to be likely signatures of the process that returns closed flux to the Sun; the combination of these processes could regulate the amount of open magnetic flux in interplanetary space. 6 refs., 3 figs

DISCONNECTION OF OPEN CORONAL MAGNETIC STRUCTURES

We have examined the Solar Maximum Mission coronagraph/polarimeter observations for evidence of magnetic disconnection of previously open magnetic structures and a number of likely examples have been found. Probable coronal disconnections typically appear as pinching off of helmet streamers followed by the release and outward acceleration of a large U or V-shaped structures. The observed sequence of events is consistent with reconnection across the heliospheric current sheet between previously open magnetic field regions, and the creation of a detached magnetic structure which is open to interplanetary space at both ends. Sunward of the reconnection point, coronal disconnection events would return previously open magnetic flux to the Sun as closed field arches. Here we (1) describe one clear disconnection event (1 June 1989); (2) examine the results of a limited survey of disconnection events; and (3) discuss the potential importance of coronal disconnections for maintaining flux in interplanetary space. 7 refs., 3 figs

On the existence of a Bose Metal at T=0

This paper aims to justify, at a microscopic level, the existence of a two-dimensional Bose metal, i.e. a metallic phase made out of Cooper pairs at T=0. To this end, we consider the physics of quantum phase fluctuations in (granular) superconductors in the absence of disorder and emphasise the role of two order parameters in the problem, viz. phase order and charge order. We focus on the 2-d Bose Hubbard model in the limit of very large fillings, i.e. a 2-d array of Josephson junctions. We find that the algebra of phase fluctuations is that of the Euclidean group $E_{2}$ in this limit, and show that the model is equivalent to two coupled XY models in (2+1)-d, one corresponding to the phase degrees of freedom, and the other the charge degrees of freedom. The Bose metal, then, is the phase in which both these degrees of freedom are disordered(as a result of quantum frustration). We analyse the model in terms of its topological excitations and suggest that there is a strong indication that this state represents a surface of critical points, akin to the gapless spin liquid states. We find a remarkable consistency of this scenario with certain low-T_c thin film experiments.Comment: 16 pages, 2 figure

A glassy contribution to the heat capacity of hcp 4^4He solids

We model the low-temperature specific heat of solid $^4$He in the hexagonal closed packed structure by invoking two-level tunneling states in addition to the usual phonon contribution of a Debye crystal for temperatures far below the Debye temperature, $T < \Theta_D/50$. By introducing a cutoff energy in the two-level tunneling density of states, we can describe the excess specific heat observed in solid hcp $^4$He, as well as the low-temperature linear term in the specific heat. Agreement is found with recent measurements of the temperature behavior of both specific heat and pressure. These results suggest the presence of a very small fraction, at the parts-per-million (ppm) level, of two-level tunneling systems in solid $^4$He, irrespective of the existence of supersolidity.Comment: 11 pages, 4 figure

Defects and glassy dynamics in solid He-4: Perspectives and current status

We review the anomalous behavior of solid He-4 at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in He-4. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid He-4. Our proposed glass model for solid He-4 has several implications: (1) The anomalous properties of He-4 can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid He-4 is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich He-4 crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in He-4.Comment: 33 pages, 13 figure