Quantum mechanics: cleaning up metaphysical baggage

The dynamic electronic structure of atoms and molecules can be directly observed by means of the (e, 2e) reaction, which measures the distribution of energies and momenta of two electrons in coincidence after a knockout reaction initiated by an electron beam of known momentum incident on a molecular gas target. The molecular state for each event is identified by the electron separation energy. The recoil momentum for each event is known from the difference of measured initial and final momenta. It has been verified that values of this momentum are equal under suitable conditions to the momentum of the electron in the target immediately before knockout. Thus the spherically-averaged electron momentum distribution for each molecular orbital is measured. This is directly related to molecular orbitals calculated by the methods of quantum chemistry. Properties obtained by this method for different types of molecules are discussed.     

Detectivity of the photosensors: A reevaluation

Important parameters of the photosensors such as Noise Equivalent Power (NEP) and detectivity depend upon the magnitude of the signal to noise ratio. Recent improvements in the techniques of measurement in digitized form permit to process noise statistically with a suitable procedure and increase the detection capability more than expected from the conventional definition.     

Energy Estimates and Cavity Interaction for a Critical‐Exponent Cavitation Model

We consider the minimization of in a perforated domain of among maps that are incompressible (det ) and invertible, and satisfy a Dirichlet boundary condition u = g on ?Ω. If the volume enclosed by g (?Ω) is greater than |Ω|, any such deformation u is forced to map the small holes B_ε( a _i) onto macroscopically visible cavities (which do not disappear as ε → 0). We restrict our attention to the critical exponent p = n, where the energy required for cavitation is of the order of and the model is suited, therefore, for an asymptotic analysis (v₁,…, v_M denote the volumes of the cavities). In the spirit of the analysis of vortices in Ginzburg‐Landau theory, we obtain estimates for the “renormalized” energy showing its dependence on the size and the shape of the cavities, on the initial distance between the cavitation points a ₁,…, a _M, and on the distance from these points to the outer boundary ?Ω. Based on those estimates we conclude, for the case of two cavities, that either the cavities prefer to be spherical in shape and well separated, or to be very close to each other and appear as a single equivalent round cavity. This is in agreement with existing numerical simulations and is reminiscent of the interaction between cavities in the mechanism of ductile fracture by void growth and coalescence. © 2012 Wiley Periodicals, Inc.     

Identification of a set of genes showing regionally enriched expression in the mouse brain

Background

We have recorded responses from single neurons in murine visual cortex to determine the effectiveness of the input from the two murine cone photoreceptor mechanisms and whether there is any unique selectivity for cone inputs at this higher region of the visual system that would support the possibility of colour vision in mice. Each eye was stimulated by diffuse light, either 370 (strong stimulus for the ultra-violet (UV) cone opsin) or 505 nm (exclusively stimulating the middle wavelength sensitive (M) cone opsin), obtained from light emitting diodes (LEDs) in the presence of a strong adapting light that suppressed the responses of rods.

Results

Single cells responded to these diffuse stimuli in all areas of striate cortex. Two types of responsive cells were encountered. One type (135/323 – 42%) had little to no spontaneous activity and responded at either the on and/or the off phase of the light stimulus with a few impulses often of relatively large amplitude. A second type (166/323 – 51%) had spontaneous activity and responded tonically to light stimuli with impulses often of small amplitude. Most of the cells responded similarly to both spectral stimuli. A few (18/323 – 6%) responded strongly or exclusively to one or the other spectral stimulus and rarely in a spectrally opponent manner.

Conclusion

Most cells in murine striate cortex receive excitatory inputs from both UV- and M-cones. A small fraction shows either strong selectivity for one or the other cone mechanism and occasionally cone opponent responses. Cells that could underlie chromatic contrast detection are present but extremely rare in murine striate cortex.     

Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals

We consider a classical system of n charged particles in an external confining potential in any dimension d ≥ 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter is of order n^?1 (mean‐field scaling). By a suitable splitting of the Hamiltonian, we extract the next‐to‐leading‐order term in the ground state energy beyond the mean‐field limit. We show that this next order term, which characterizes the fluctuations of the system, is governed by a new “renormalized energy” functional providing a way to compute the total Coulomb energy of a jellium (i.e., an infinite set of point charges screened by a uniform neutralizing background) in any dimension. The renormalization that cuts out the infinite part of the energy is achieved by smearing out the point charges at a small scale, as in Onsager's lemma. We obtain consequences for the statistical mechanics of the Coulomb gas: next‐to‐leading‐order asymptotic expansion of the free energy or partition function, characterizations of the Gibbs measures, estimates on the local charge fluctuations, and factorization estimates for reduced densities. This extends results of Sandier and Serfaty to dimension higher than 2 by an alternative approach. © 2016 Wiley Periodicals, Inc.     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.