An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here on the case of time series data that can ultimately be modelled as a spatially distributed system (e.g. a partial differential equation, PDE), but where we do not know the space in which this PDE should be formulated. Hence, even the spatial coordinates for the distributed system themselves need to be identified - to emerge from - the data mining process. We will first validate this emergent space reconstruction for time series sampled without space labels in known PDEs; this brings up the issue of observability of physical space from temporal observation data, and the transition from spatially resolved to lumped (order-parameter-based) representations by tuning the scale of the data mining kernels. We will then present actual emergent space discovery illustrations. Our illustrative examples include chimera states (states of coexisting coherent and incoherent dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics, arising in partial differential equations and/or in heterogeneous networks. We also discuss how data-driven spatial coordinates can be extracted in ways invariant to the nature of the measuring instrument. Such gauge-invariant data mining can go beyond the fusion of heterogeneous observations of the same system, to the possible matching of apparently different systems

Formation of titanium nitride, titanium carbide, and silicon carbide surfaces by high power femtosecond laser treatment

Coatings based on titanium nitrides, titanium carbides and silicon carbides can optimize the surface properties of titanium or silicon for various applications ranging from biocompatibility to chemical stability and durability. Here, we investigated a high power (100 W) high pulse repetition rate femtosecond laser process (λ=1030 nm, τ=750 fs, f=1 MHz) for the treatment of titanium and silicon in atmospheres of argon, nitrogen, methane, ethene and acetylene. In a nitrogen atmosphere, a homogeneous coating of TiON is formed on titanium. In an ethene/argon atmosphere coatings of TiOC and SiC are formed on Ti and Si, respectively. The process allows a fast surface transformation with a process rate of 0.33 cm2 s−1 and a high spatial resolution below 0.5 mm with a minimal heat affected zone at the same time. In contrast to low repetition rate femtosecond laser processed samples, the surfaces are more robust against mechanical impact. At the same time, the surfaces reveal a distinct microstructure in comparison to coatings obtained by vapor deposition techniques

Customizing the appearance of sparks with binary metal alloys

Long-flying sparks are an essential part of several pyrotechnic effects. Unfortunately, and in contrast to colored flames, the color space of sparks is basically limited to the black-body curve. With low-boiling metals, vapor phase combustion and bright colorful flashes are achievable. In 1999, alloys of rare-earth elements have been proposed for colorful spark genera-tion. To the best of our knowledge, here we present the first investigation of such alloys to change the color of sparks be-yond the black-body limit. Alloys consisting of >65 at.-% of a brightly emitting and low-boiling metal and a carrier metal allow achieving long-flying deeply colored sparks. Besides the color, branching of sparks is crucial for the visual appear-ance. Rare-earth metals were found to promote branching of different alloys. Finally, fountains ejecting golden/green sparks based on a stable eutectic Yb-Cu alloy and continuously branching sparks based on Nd2Fe14B are presented

DNA hybridization to mismatched templates: a chip study

High-density oligonucleotide arrays are among the most rapidly expanding technologies in biology today. In the {\sl GeneChip} system, the reconstruction of the target concentration depends upon the differential signal generated from hybridizing the target RNA to two nearly identical templates: a perfect match (PM) and a single mismatch (MM) probe. It has been observed that a large fraction of MM probes repeatably bind targets better than the PMs, against the usual expectation from sequence-specific hybridization; this is difficult to interpret in terms of the underlying physics. We examine this problem via a statistical analysis of a large set of microarray experiments. We classify the probes according to their signal to noise ($S/N$) ratio, defined as the eccentricity of a (PM, MM) pair's `trajectory' across many experiments. Of those probes having large $S/N$ ($>3$) only a fraction behave consistently with the commonly assumed hybridization model. Our results imply that the physics of DNA hybridization in microarrays is more complex than expected, and they suggest new ways of constructing estimators for the target RNA concentration.Comment: 3 figures 1 tabl

A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms

Meta-learning of numerical algorithms for a given task consist of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters. To limit the complexity of the meta-learning problem, neural architectures with a certain inductive bias towards favorable algorithmic structures can, and should, be used. We generalize our previously introduced Runge-Kutta neural network to a recursively recurrent neural network (R2N2) superstructure for the design of customized iterative algorithms. In contrast to off-the-shelf deep learning approaches, it features a distinct division into modules for generation of information and for the subsequent assembly of this information towards a solution. Local information in the form of a subspace is generated by subordinate, inner, iterations of recurrent function evaluations starting at the current outer iterate. The update to the next outer iterate is computed as a linear combination of these evaluations, reducing the residual in this space, and constitutes the output of the network. We demonstrate that regular training of the weight parameters inside the proposed superstructure on input/output data of various computational problem classes yields iterations similar to Krylov solvers for linear equation systems, Newton-Krylov solvers for nonlinear equation systems, and Runge-Kutta integrators for ordinary differential equations. Due to its modularity, the superstructure can be readily extended with functionalities needed to represent more general classes of iterative algorithms traditionally based on Taylor series expansions.Comment: manuscript (21 pages, 10 figures), supporting information (2 pages, 1 figure

Monoamine Oxidase A is Required for Rapid Dendritic Remodeling in Response to Stress

Background: Acute stress triggers transient alterations in the synaptic release and metabolism of brain monoamine neurotransmitters. These rapid changes are essential to activate neuroplastic processes aimed at the appraisal of the stressor and enactment of commensurate defensive behaviors. Threat evaluation has been recently associated with the dendritic morphology of pyramidal cells in the orbitofrontal cortex (OFC) and basolateral amygdala (BLA); thus, we examined the rapid effects of restraint stress on anxiety-like behavior and dendritic morphology in the BLA and OFC of mice. Furthermore, we tested whether these processes may be affected by deficiency of monoamine oxidase A (MAO-A), the primary enzyme catalyzing monoamine metabolism. Methods: Following a short-term (1–4h) restraint schedule, MAO-A knockout (KO) and wild-type (WT) mice were sacrificed, and histological analyses of dendrites in pyramidal neurons of the BLA and OFC of the animals were performed. Anxiety-like behaviors were examined in a separate cohort of animals subjected to the same experimental conditions. Results: In WT mice, short-term restraint stress significantly enhanced anxiety-like responses, as well as a time-dependent proliferation of apical (but not basilar) dendrites of the OFC neurons; conversely, a retraction in BLA dendrites was observed. None of these behavioral and morphological changes were observed in MAO-A KO mice. Conclusions: These findings suggest that acute stress induces anxiety-like responses by affecting rapid dendritic remodeling in the pyramidal cells of OFC and BLA; furthermore, our data show that MAO-A and monoamine metabolism are required for these phenomena

Early postnatal inhibition of serotonin synthesis results in long-term reductions of perseverative behaviors, but not aggression, in MAO A-deficient mice

Monoamine oxidase (MAO) A, the major enzyme catalyzing the oxidative degradation of serotonin (5-hydroxytryptamine, 5-HT), plays a key role in emotional regulation. In humans and mice, MAO-A deficiency results in high 5-HT levels, antisocial, aggressive, and perseverative behaviors. We previously showed that the elevation in brain 5-HT levels in MAO-A knockout (KO) mice is particularly marked during the first two weeks of postnatal life. Building on this finding, we hypothesized that the reduction of 5-HT levels during these early stages may lead to enduring attenuations of the aggression and other behavioral aberrances observed in MAO-A KO mice. To test this possibility, MAO-A KO mice were treated with daily injections of a 5-HT synthesis blocker, the tryptophan hydroxylase inhibitor p-chloro-phenylalanine (pCPA, 300 mg/kg/day, IP), from postnatal day 1 through 7. As expected, this regimen significantly reduced 5-HT forebrain levels in MAO-A KO pups. These neurochemical changes persisted throughout adulthood, and resulted in significant reductions in marble-burying behavior, as well as increases in spontaneous alternations within a T-maze. Conversely, pCPA-treated MAO-A KO mice did not exhibit significant changes in anxiety-like behaviors in a novel open-field and elevated plus-maze; furthermore, this regimen did not modify their social deficits, aggressive behaviors and impairments in tactile sensitivity. Treatment with pCPA from postnatal day 8 through 14 elicited similar, yet milder, behavioral effects on marble-burying behavior. These results suggest that early developmental enhancements in 5-HT levels have long-term effects on the modulation of behavioral flexibility associated with MAO-A deficiency

Stress‐Actuated Spiral Microelectrode for High‐Performance Lithium‐Ion Microbatteries

Miniaturization of batteries lags behind the success of modern electronic devices. Neither the device volume nor the energy density of microbatteries meets the requirement of microscale electronic devices. The main limitation for pushing the energy density of microbatteries arises from the low mass loading of active materials. However, merely pushing the mass loading through increased electrode thickness is accompanied by the long charge transfer pathway and inferior mechanical properties for long‐term operation. Here, a new spiral microelectrode upon stress‐actuation accomplishes high mass loading but short charge transfer pathways. At a small footprint area of around 1 mm2, a 21‐fold increase of the mass loading is achieved while featuring fast charge transfer at the nanoscale. The spiral microelectrode delivers a maximum area capacity of 1053 µAh cm−2 with a retention of 67% over 50 cycles. Moreover, the energy density of the cylinder microbattery using the spiral microelectrode as the anode reaches 12.6 mWh cm−3 at an ultrasmall volume of 3 mm3. In terms of the device volume and energy density, the cylinder microbattery outperforms most of the current microbattery technologies, and hence provides a new strategy to develop high‐performance microbatteries that can be integrated with miniaturized electronic devices