A Method for Calibration of the Local Magnitude Scale Based on Relative Spectral Amplitudes, and Application to the San Juan Bautista, California, Area

We develop and use a spectral empirical Green’s function approach to estimate the relative source amplitudes of earthquakes near San Juan Bautista, California. We isolate the source amplitudes from path effects by comparing the recorded spectra of pairs of events with similar location and focal mechanism, without computing the path effect. With this method, we estimate the relative moments of 1600 M 1.5–4 local earthquakes, and we use these moments to recalibrate the duration magnitude scale in this region. The estimated moments of these small earthquakes increase with catalog magnitude MD roughly proportionally to 101.1MD, slightly more slowly than a moment‐magnitude scaling of 101.5Mw. This more accurate magnitude scaling can be used in analyses of the local earthquakes, such as comparisons between the seismic moments and geodetic observations

Relationships and events: towards a general theory of reification and truthmaking.

We propose a novel ontological analysis of relations and relationships based on a re-visitation of a classic problem in the practice of knowledge repre- sentation and conceptual modeling, namely relationship reification. Our idea is that a relation holds in virtue of a relationship's existence. Relationships are therefore truthmakers of relations. In this paper we present a general theory or reification and truthmaking, and discuss the interplay between events and rela- tionships, suggesting that relationships are the focus of events, which emerge from the context (the scene) they occur in

Scaling properties of protein family phylogenies

One of the classical questions in evolutionary biology is how evolutionary processes are coupled at the gene and species level. With this motivation, we compare the topological properties (mainly the depth scaling, as a characterization of balance) of a large set of protein phylogenies with a set of species phylogenies. The comparative analysis shows that both sets of phylogenies share remarkably similar scaling behavior, suggesting the universality of branching rules and of the evolutionary processes that drive biological diversification from gene to species level. In order to explain such generality, we propose a simple model which allows us to estimate the proportion of evolvability/robustness needed to approximate the scaling behavior observed in the phylogenies, highlighting the relevance of the robustness of a biological system (species or protein) in the scaling properties of the phylogenetic trees. Thus, the rules that govern the incapability of a biological system to diversify are equally relevant both at the gene and at the species level.Comment: Replaced with final published versio

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Contrasting prefrontal cortex contributions to episodic memory dysfunction in behavioural variant frontotemporal dementia and alzheimer's disease

Recent evidence has questioned the integrity of episodic memory in behavioural variant frontotemporal dementia (bvFTD), where recall performance is impaired to the same extent as in Alzheimer's disease (AD). While these deficits appear to be mediated by divergent patterns of brain atrophy, there is evidence to suggest that certain prefrontal regions are implicated across both patient groups. In this study we sought to further elucidate the dorsolateral (DLPFC) and ventromedial (VMPFC) prefrontal contributions to episodic memory impairment in bvFTD and AD. Performance on episodic memory tasks and neuropsychological measures typically tapping into either DLPFC or VMPFC functions was assessed in 22 bvFTD, 32 AD patients and 35 age- and education-matched controls. Behaviourally, patient groups did not differ on measures of episodic memory recall or DLPFC-mediated executive functions. BvFTD patients were significantly more impaired on measures of VMPFC-mediated executive functions. Composite measures of the recall, DLPFC and VMPFC task scores were covaried against the T1 MRI scans of all participants to identify regions of atrophy correlating with performance on these tasks. Imaging analysis showed that impaired recall performance is associated with divergent patterns of PFC atrophy in bvFTD and AD. Whereas in bvFTD, PFC atrophy covariates for recall encompassed both DLPFC and VMPFC regions, only the DLPFC was implicated in AD. Our results suggest that episodic memory deficits in bvFTD and AD are underpinned by divergent prefrontal mechanisms. Moreover, we argue that these differences are not adequately captured by existing neuropsychological measures

Role of mitochondrial raft-like microdomains in the regulation of cell apoptosis

Lipid rafts are envisaged as lateral assemblies of specific lipids and proteins that dissociate and associate rapidly and form functional clusters in cell membranes. These structural platforms are not confined to the plasma membrane; indeed lipid microdomains are similarly formed at subcellular organelles, which include endoplasmic reticulum, Golgi and mitochondria, named raft-like microdomains. In addition, some components of raft-like microdomains are present within ER-mitochondria associated membranes. This review is focused on the role of mitochondrial raft-like microdomains in the regulation of cell apoptosis, since these microdomains may represent preferential sites where key reactions take place, regulating mitochondria hyperpolarization, fission-associated changes, megapore formation and release of apoptogenic factors. These structural platforms appear to modulate cytoplasmic pathways switching cell fate towards cell survival or death. Main insights on this issue derive from some pathological conditions in which alterations of microdomains structure or function can lead to severe alterations of cell activity and life span. In the light of the role played by raft-like microdomains to integrate apoptotic signals and in regulating mitochondrial dynamics, it is conceivable that these membrane structures may play a role in the mitochondrial alterations observed in some of the most common human neurodegenerative diseases, such as Amyotrophic lateral sclerosis, Huntington's chorea and prion-related diseases. These findings introduce an additional task for identifying new molecular target(s) of pharmacological agents in these pathologies

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Neural Computation via Neural Geometry: A Place Code for Inter-whisker Timing in the Barrel Cortex?

The place theory proposed by Jeffress (1948) is still the dominant model of how the brain represents the movement of sensory stimuli between sensory receptors. According to the place theory, delays in signalling between neurons, dependent on the distances between them, compensate for time differences in the stimulation of sensory receptors. Hence the location of neurons, activated by the coincident arrival of multiple signals, reports the stimulus movement velocity. Despite its generality, most evidence for the place theory has been provided by studies of the auditory system of auditory specialists like the barn owl, but in the study of mammalian auditory systems the evidence is inconclusive. We ask to what extent the somatosensory systems of tactile specialists like rats and mice use distance dependent delays between neurons to compute the motion of tactile stimuli between the facial whiskers (or ‘vibrissae’). We present a model in which synaptic inputs evoked by whisker deflections arrive at neurons in layer 2/3 (L2/3) somatosensory ‘barrel’ cortex at different times. The timing of synaptic inputs to each neuron depends on its location relative to sources of input in layer 4 (L4) that represent stimulation of each whisker. Constrained by the geometry and timing of projections from L4 to L2/3, the model can account for a range of experimentally measured responses to two-whisker stimuli. Consistent with that data, responses of model neurons located between the barrels to paired stimulation of two whiskers are greater than the sum of the responses to either whisker input alone. The model predicts that for neurons located closer to either barrel these supralinear responses are tuned for longer inter-whisker stimulation intervals, yielding a topographic map for the inter-whisker deflection interval across the surface of L2/3. This map constitutes a neural place code for the relative timing of sensory stimuli