Continuous limits of residual neural networks in case of large input data

Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean-field limit and show well-posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

COMPETITION AMONG HOSPITALS AND ITS MEASUREMENT: THEORY AND A CASE STUDY

Our paper provides several insights on the characteristics of the concept of “Poles d’Excellence Rurale” (PER) through bilateral comparisons with that of Competitive Pole (CP) and cluster. The concept of PER is a French government’ initiative designed for the development of rural areas similar to that of the Competitive Pole. We emphasize important particularities of these concepts by analyzing some of their similarities and major differences.Pole d’Excellence Rurale, Competitive Pole, cluster, rural development

Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling

In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated periodically by $\delta$-kicks which represents a realization of a kicked top. In the (classical) mean-field approximation it provides a rich mixed phase space dynamics with regular and chaotic regions. By increasing the kick-strength a bifurcation leads to the appearance of self-trapping states localized on regular islands. This self-trapping is also found for the many particle system, however in general suppressed by coherent many particle tunneling oscillations. The tunneling time can be calculated from the quasi-energy splitting of the corresponding Floquet states. By varying the kick-strength these quasi-energy levels undergo both avoided and even actual crossings. Therefore stimulation or complete destruction of tunneling can be observed for this many particle system

Gas phase formation of extremely oxidized pinene reaction products in chamber and ambient air

High molecular weight (300–650 Da) naturally charged negative ions have previously been observed at a boreal forest site in Hyytiälä, Finland. The long-term measurements conducted in this work showed that these ions are observed practically every night between spring and autumn in Hyytiälä. The ambient mass spectral patterns could be reproduced in striking detail during additional measurements of α-pinene (C<sub>10</sub>H<sub>16</sub>) oxidation at low-OH conditions in the Jülich Plant Atmosphere Chamber (JPAC). The ions were identified as clusters of the nitrate ion (NO<sub>3</sub><sup>−</sup>) and α-pinene oxidation products reaching oxygen to carbon ratios of 0.7–1.3, while retaining most of the initial ten carbon atoms. Attributing the ions to clusters instead of single molecules was based on additional observations of the same extremely oxidized organics in clusters with HSO<sub>4</sub><sup>−</sup> (Hyytiälä) and C<sub>3</sub>F<sub>5</sub>O<sub>2</sub><sup>−</sup> (JPAC). The most abundant products in the ion spectra were identified as C<sub>10</sub>H<sub>14</sub>O<sub>7</sub>, C<sub>10</sub>H<sub>14</sub>O<sub>9</sub>, C<sub>10</sub>H<sub>16</sub>O<sub>9</sub>, and C<sub>10</sub>H<sub>14</sub>O<sub>11</sub>. The mechanism responsible for forming these molecules is still not clear, but the initial reaction is most likely ozone attack at the double bond, as the ions are mainly observed under dark conditions. β-pinene also formed highly oxidized products under the same conditions, but less efficiently, and mainly C<sub>9</sub> compounds which were not observed in Hyytiälä, where β-pinene on average is 4–5 times less abundant than α-pinene. Further, to explain the high O/C together with the relatively high H/C, we propose that geminal diols and/or hydroperoxide groups may be important. We estimate that the night-time concentration of the sum of the neutral extremely oxidized products is on the order of 0.1–1 ppt (~10<sup>6</sup>–10<sup>7</sup> molec cm<sup>−3</sup>). This is in a similar range as the amount of gaseous H<sub>2</sub>SO<sub>4</sub> in Hyytiälä during day-time. As these highly oxidized organics are roughly 3 times heavier, likely with extremely low vapor pressures, their role in the initial steps of new aerosol particle formation and growth may be important and needs to be explored in more detail in the future

The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

Comparison of emission ratios from on-road sources using a mobile laboratory under various driving and operational sampling modes

International audienceMobile sources produce a significant fraction of the total anthropogenic emissions burden in large cities and have harmful effects on air quality at multiple spatial scales. Mobile emissions are intrinsically difficult to estimate due to the large number of parameters affecting the emissions variability within and across vehicles types. The MCMA-2003 Campaign in Mexico City has showed the utility of using a mobile laboratory to sample and characterize specific classes of motor vehicles to better quantify their emissions characteristics as a function of their driving cycles. The technique clearly identifies "high emitter" vehicles via individual exhaust plumes, and also provides fleet average emission rates. We have applied this technique to Mexicali during the Border Ozone Reduction and Air Quality Improvement Program for the Mexicali-Imperial Valley in 2005. In this paper we analyze the variability of measured emission ratios for emitted NOx, CO, specific VOCs, NH3, and some primary fine particle components and properties obtained during the Border Ozone Reduction and Air Quality Improvement Program for the Mexicali-Imperial Valley in 2005 by deploying a mobile laboratory in roadside stationary sampling, chase and fleet average operational sampling modes. The measurements reflect various driving modes characteristic of the urban fleets. The observed variability for all measured gases and particle emission ratios is greater for the chase and roadside stationary sampling than for fleet average measurements. The fleet average sampling mode captured the effects of traffic conditions on the measured on-road emission ratios, allowing the use of fuel-based emission ratios to assess the validity of traditional "bottom-up" emissions inventories. Using the measured on-road emission ratios, we estimate CO and NOx mobile emissions of 175±62 and 10.4±1.3 metric tons/day, respectively, for the gasoline vehicle fleet in Mexicali. Comparisons with similar on-road emissions data from Mexico City indicated that fleet average NO emission ratios were around 20% higher in Mexicali than in Mexico City whereas HCHO and NH3 emission ratios were higher by a factor of 2 in Mexico City than in Mexicali. Acetaldehyde emission ratios did not differ significantly whereas selected aromatics VOCs emissions were similar or smaller in Mexicali. On-road heavy-duty diesel truck (HDDT) nitrogen oxides emissions were measured near Austin, Texas, as well as in both Mexican cities, with NOy emission ratios in Austin < Mexico City < Mexicali

Comparison of emissions from on-road sources using a mobile laboratory under various driving and operational sampling modes

Mobile sources produce a significant fraction of the total anthropogenic emissions burden in large cities and have harmful effects on air quality at multiple spatial scales. Mobile emissions are intrinsically difficult to estimate due to the large number of parameters affecting the emissions variability within and across vehicles types. The MCMA-2003 Campaign in Mexico City has showed the utility of using a mobile laboratory to sample and characterize specific classes of motor vehicles to better quantify their emissions characteristics as a function of their driving cycles. The technique clearly identifies "high emitter" vehicles via individual exhaust plumes, and also provides fleet average emission rates. We have applied this technique to Mexicali during the Border Ozone Reduction and Air Quality Improvement Program (BORAQIP) for the Mexicali-Imperial Valley in 2005. We analyze the variability of measured emission ratios for emitted NOx [NO subscript x], CO, specific VOCs, NH3 [NH subscript 3], and some primary fine particle components and properties by deploying a mobile laboratory in roadside stationary sampling, chase and fleet average operational sampling modes. The measurements reflect various driving modes characteristic of the urban fleets. The observed variability for all measured gases and particle emission ratios is greater for the chase and roadside stationary sampling than for fleet average measurements. The fleet average sampling mode captured the effects of traffic conditions on the measured on-road emission ratios, allowing the use of fuel-based emission ratios to assess the validity of traditional "bottom-up" emissions inventories. Using the measured on-road emission ratios, we estimate CO and NOx [NO subscript x] mobile emissions of 175±62 and 10.4±1.3 metric tons/day, respectively, for the gasoline vehicle fleet in Mexicali. Comparisons with similar on-road emissions data from Mexico City indicated that fleet average NO emission ratios were around 20% higher in Mexicali than in Mexico City whereas HCHO and NH3 [NH subscript 3] emission ratios were higher by a factor of 2 in Mexico City than in Mexicali. Acetaldehyde emission ratios did not differ significantly whereas selected aromatics VOCs emissions were similar or smaller in Mexicali. Nitrogen oxides emissions for on-road heavy-duty diesel truck (HDDT) were measured near Austin, Texas, as well as in both Mexican cities, with NOy [NO subscript y] emission ratios in Austin < Mexico City < Mexicali.Mexico. Comisión Ambiental MetropolitanaNational Science Foundation (U.S.) (Grant ATM-0528227)Molina Center for Energy and the EnvironmentUniversity of Texas at AustinLatin American Scholarship Program of American Universitie

Previously described sequence variant in CDK5RAP2 gene in a Pakistani family with autosomal recessive primary microcephaly

<p>Abstract</p> <p>Background</p> <p>Autosomal Recessive Primary Microcephaly (MCPH) is a disorder of neurogenic mitosis. MCPH leads to reduced cerebral cortical volume and hence, reduced head circumference associated with mental retardation of variable degree. Genetic heterogeneity is well documented in patients with MCPH with six loci known, while pathogenic sequence variants in four respective genes have been identified so far. Mutations in <it>CDK5RAP2 </it>gene at MCPH3 locus have been least involved in causing MCPH phenotype.</p> <p>Methods</p> <p>All coding exons and exon/intron splice junctions of <it>CDK5RAP2 </it>gene were sequenced in affected and normal individuals of Pakistani MCPH family of Kashmiri origin, which showed linkage to MCPH3 locus on chromosome 9q33.2.</p> <p>Results</p> <p>A previously described nonsense mutation [243 T>A (S81X)] in exon 4 of <it>CDK5RAP2 </it>gene has been identified in the Pakistani family, presented here, with MCPH Phenotype. Genomic and cDNA sequence comparison revealed that the exact nomenclature for this mutation is 246 T>A (Y82X).</p> <p>Conclusion</p> <p>Recurrent observation of Y82X mutation in <it>CDK5RAP2 </it>gene in this Pakistani family may be a sign of confinement of a rare ancestral haplotype carrying this pathogenic variant within Northern Pakistani population, as this has not been reported in any other population.</p

Responses of marine benthic microalgae to elevated CO<inf>2</inf>

Increasing anthropogenic CO2 emissions to the atmosphere are causing a rise in pCO2 concentrations in the ocean surface and lowering pH. To predict the effects of these changes, we need to improve our understanding of the responses of marine primary producers since these drive biogeochemical cycles and profoundly affect the structure and function of benthic habitats. The effects of increasing CO2 levels on the colonisation of artificial substrata by microalgal assemblages (periphyton) were examined across a CO2 gradient off the volcanic island of Vulcano (NE Sicily). We show that periphyton communities altered significantly as CO2 concentrations increased. CO2 enrichment caused significant increases in chlorophyll a concentrations and in diatom abundance although we did not detect any changes in cyanobacteria. SEM analysis revealed major shifts in diatom assemblage composition as CO2 levels increased. The responses of benthic microalgae to rising anthropogenic CO2 emissions are likely to have significant ecological ramifications for coastal systems. © 2011 Springer-Verlag