Constructing stochastic models for dipole fluctuations from paleomagnetic observations

Records of relative paleointensity are subject to several sources of error. Temporal averaging due to gradual acquisition of magnetization removes high-frequency fluctuations, whereas random errors introduce fluctuations at high frequency. Both sources of error limit our ability to construct stochastic models from paleomagnetic observations. We partially circumvent these difficulties by recognizing that the largest affects occur at high frequency. To illustrate we construct a stochastic model from two recent inversions of paleomagnetic observations for the axial dipole moment. An estimate of the noise term in the stochastic model is recovered from a high-resolution inversion (CALS10k.2), while the drift term is estimated from the low-frequency part of the power spectrum for a long, but lower-resolution inversion (PADM2M). Realizations of the resulting stochastic model yield a composite, broadband power spectrum that agrees well with the spectra from both PADM2M and CALS10k.2. A simple generalization of the stochastic model permits predictions for the mean rate of magnetic reversals. We show that the reversal rate depends on the time-averaged dipole moment, the variance of the dipole moment and a slow timescale that characterizes the adjustment of the dipole toward the time-averaged value. Predictions of the stochastic model give a mean rate of 4.2 Myr^(−1), which is in good agreement with observations from marine magnetic anomalies

Lifted Inference for Convex Quadratic Programs

Symmetry is the essential element of lifted inferencethat has recently demonstrated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models. This raises the question, whether this holds for optimization problems in general.Here we show that for a large classof optimization methods this is actually the case.Specifically, we introduce the concept of fractionalsymmetries of convex quadratic programs (QPs),which lie at the heart of many AI and machine learning approaches,and exploit it to lift, i.e., to compress QPs.These lifted QPs can then be tackled with the usual optimization toolbox (off-the-shelf solvers, cutting plane algorithms,stochastic gradients etc.). If the original QP exhibitssymmetry, then the lifted one will generallybe more compact, and hence more efficient to solve

Quantifying geological processes on Mars—Results of the high resolution stereo camera (HRSC) on Mars express

This review summarizes the use of High Resolution Stereo Camera (HRSC) data as an instrumental tool and its application in the analysis of geological processes and landforms on Mars during the last 10 years of operation. High-resolution digital elevations models on a local to regional scale are the unique strength of the HRSC instrument. The analysis of these data products enabled quantifying geological processes such as effusion rates of lava flows, tectonic deformation, discharge of water in channels, formation timescales of deltas, geometry of sedimentary deposits as well as estimating the age of geological units by crater size–frequency distribution measurements. Both the quantification of geological processes and the age determination allow constraining the evolution of Martian geologic activity in space and time. A second major contribution of HRSC is the discovery of episodicity in the intensity of geological processes on Mars. This has been revealed by comparative age dating of volcanic, fluvial, glacial, and lacustrine deposits. Volcanic processes on Mars have been active over more than 4 Gyr, with peak phases in all three geologic epochs, generally ceasing towards the Amazonian. Fluvial and lacustrine activity phases spread a time span from Noachian until Amazonian times, but detailed studies show that they have been interrupted by multiple and long lasting phases of quiescence. Also glacial activity shows discrete phases of enhanced intensity that may correlate with periods of increased spin-axis obliquity. The episodicity of geological processes like volcanism, erosion, and glaciation on Mars reflects close correlation between surface processes and endogenic activity as well as orbit variations and changing climate condition

Face processing as a brain adaptation at multiple timescales

[Formula: see text] I consider face processing as the brain's adaptive response to phylogenetic, ontogenetic, and task-specific factors. Focusing on wide-ranging evidence from both my own laboratory and others, evidence for a primitive "quick and dirty" route for face processing that exists prior to postnatal experience is reviewed. Next, I trace the emergence of cortical specialization for face processing influenced by individual developmental experience (ontogenetic adaptation) and suggest that this ontogenetic adaptation is also heavily constrained by the phylogenetic system. Finally, I turn to recent evidence on task-specific modulation of activity in the core face network that illustrates brain adaptation at a finer timescale than that for the other systems. Current evidence indicates that task-specific modulation of the cortical face network does not emerge until the teenage years. As previously proposed for other components of cognition, I propose that these systems are complementary to each other, each compensating for the others' weaknesses. Different face-related systems are adapted to respond to survival pressures at different timescales, from millennia, to months, to microseconds