Large Deviations, Dynamics and Phase Transitions in Large Stochastic and Disordered Neural Networks

Neuronal networks are characterized by highly heterogeneous connectivity, and this disorder was recently related experimentally to qualitative properties of the network. The motivation of this paper is to mathematically analyze the role of these disordered connectivities on the large-scale properties of neuronal networks. To this end, we analyze here large-scale limit behaviors of neural networks including, for biological relevance, multiple populations, random connectivities and interaction delays. Due to the randomness of the connectivity, usual mean-field methods (e.g. coupling) cannot be applied, but, similarly to studies developed for spin glasses, we will show that the sequences of empirical measures satisfy a large deviation principle, and converge towards a self-consistent non-Markovian process. From a mathematical viewpoint, the proof differs from previous works in that we are working in infinite-dimensional spaces (interaction delays) and consider multiple cell types. The limit obtained formally characterizes the macroscopic behavior of the network. We propose a dynamical systems approach in order to address the qualitative nature of the solutions of these very complex equations, and apply this methodology to three instances in order to show how non-centered coefficients, interaction delays and multiple populations networks are affected by disorder levels. We identify a number of phase transitions in such systems upon changes in delays, connectivity patterns and dispersion, and particularly focus on the emergence of non-equilibrium states involving synchronized oscillations.     

Identifying the radiating core of Lighthill’s source term

A decomposition of the Lighthill source term is effected which yields ten sub-terms comprising velocity, vorticity, dilatation and density fields. An analysis methodology is then developed, aimed at understanding the respective roles played by these sub-terms in the production of sound. By Direct Numerical Simulation of a temporal mixing-layer—chosen both for its simplicity and its amenability to analysis in wavenumber space—the radiating components of the different sub-terms are isolated and studied. Interesting identities are observed between specific events in the evolution of the flow and the various sub-terms of the source, and the essence of the sound production mechanism is found to comprise subtle imbalances which disrupt inherent space–time symmetries which exist between the various sub-terms.      

Three‐dimensional imaging of chemical phase transformations at the nanoscale with full‐field transmission X‐ray microscopy

The ability to probe morphology and phase distribution in complex systems at multiple length scales unravels the interplay of nano‐ and micrometer‐scale factors at the origin of macroscopic behavior. While different electron‐ and X‐ray‐based imaging techniques can be combined with spectroscopy at high resolutions, owing to experimental time limitations the resulting fields of view are too small to be representative of a composite sample. Here a new X‐ray imaging set‐up is proposed, combining full‐field transmission X‐ray microscopy (TXM) with X‐ray absorption near‐edge structure (XANES) spectroscopy to follow two‐dimensional and three‐dimensional morphological and chemical changes in large volumes at high resolution (tens of nanometers). TXM XANES imaging offers chemical speciation at the nanoscale in thick samples (>20 µm) with minimal preparation requirements. Further, its high throughput allows the analysis of large areas (up to millimeters) in minutes to a few hours. Proof of concept is provided using battery electrodes, although its versatility will lead to impact in a number of diverse research fields.     

The vibration-rotation spectrum of methinophosphide: The overtone bands 2ν1 and 2ν3, the summation bands ν1 + ν2 and ν2 + ν3, and the difference band ν1 - ν2

The vibration-rotation bands 2ν₁, 2ν₃, ν₁ + ν₂, ν₂ + ν₃, and ν₁ - ν₂ of H¹²CP were recorded and analyzed. These data were combined with previously reported results for this molecule to obtain an improved and extended set of vibrational and rotational constants. All x_ij and γ_ij were calculated except those that require data from a summation band involving ν₁ and ν₃.     

High resolution infrared spectra and structure of borine carbonyl: The analysis of the ν2 bands of 11BD3CO and 10BD3CO

The high resolution infrared spectra of ¹⁰BD₃CO and ¹¹BD₃CO were obtained in the region of the ν₂ fundamentals. The K = 0 subbands of the ν₂ and ν₂ + ν₈ ? ν₈ bands were assigned. The K structure is unresolvable with a spectral slit width of 0.03 cm^?1. A series, almost as strong as the main series, has been identified in the spectrum of the ¹¹B molecule but has not been assigned. It is shown that the four structural parameters of borine carbonyl cannot be accurately determined using only the B₀ rotational constants of four isotopically substituted molecules.     

The vibration-rotation spectrum of methinophosphide: l-Type doubling, l-type resonance and the ν2, 2ν2, and 3ν2 bands of H12CP; The ν1 and ν2 bands of H13CP

The vibration-rotation bands ν₂, 2ν₂, and several “hot” bands of H¹²CP have been recorded and assigned. The states with v₂ = 2, perturbed by l-type resonance and l-type doubling effects have been analyzed on the basis of the existing theory. The energy difference between the 02²0 and the 02⁰0 states was found to be 17.5095 (19) cm^?1. Because of insufficient data, the states with v₂ = 3 could not be corrected for l-type resonance interaction and therefore only an effective l-type doubling constant was obtained. The ν₁ and ν₂ bands of the H¹³CP isotopic molecule (present at natural concentration) were also identified and their spectroscopic constants obtained. The value of I_e for H¹²CP is found to be 25.18793 (26) amu Ų.     

High rate performance of lithium manganese nitride and oxynitride as negative electrodes in lithium batteries

The performance of Li_7.9MnN_3.2O_1.6 and Li₇MnN₄ as electrode materials in lithium batteries was analyzed. At 1C rate, capacities of 180 and 230 mAh/g, respectively, were obtained after 50 cycles. If the first charge is done at 0.1C, outstanding capacities of 120–135 mAh/g are observed after 100 cycles at 5C. More lithium can be removed during the charge at 0.1C, leading to a large amount of lithium vacancies that enhance mobility and rate capability. It is proposed that incomplete filling of the vacancies occurs upon cycling, so that the mobility remains high. This performance compares well to that of Li₄Ti₅O₁₂.     

High-resolution infrared spectrum of carbon suboxide: The ν4 + 2ν70 and ν4 + 3ν71 − ν71 bands

The infrared spectrum of the ν₄ + 2ν₇ progression of C₃O₂ has been recorded with a resolution of about 0.018 cm^?1. Two bands of the progression have been completely analyzed. The band centers obtained in this study establish, when combined with previously published experimental results, than 3ν₇¹ is 97.22 cm^?1 above the ground vibrational state.     

High-resolution infrared spectrum of CH2D2: The ν3 fundamental band at 7 μm

The infrared spectrum of CH₂D₂ has been recorded in the region of 1345 to 1561 cm^?1 with a resolution of 0.030 to 0.026 cm^?1. Most of the observed lines have been assigned to transitions of the ν₃ band of CH₂D₂. However, 114 lines have been identified as transitions of the ν₂ band of H₂¹⁶O whose band origin has been directly determined to be 1594.7472 ± 0.0030 cm^?1. A few weak lines, probably belonging to the ν₅ fundamental of CH₂D₂, remain unassigned. The band center ν = 1435.1326 ± 0.0030 cm^?1 and a set of upper state constants were obtained for the ν₃ band of CH₂D₂. Although a slight perturbation was noticed in the ν₃ band, all wavenumbers have been fitted with a standard deviation of 3.8 × 10^?3 cm^?1.