Statistics of weighted Poisson events and its applications

The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD.Comment: 14 pages, 2 figure

Identifiability and Unmixing of Latent Parse Trees

This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian matrix, and apply it to several standard constituency and dependency parsing models. Second, for identifiable models, how do we estimate the parameters efficiently? EM suffers from local optima, while recent work using spectral methods cannot be directly applied since the topology of the parse tree varies across sentences. We develop a strategy, unmixing, which deals with this additional complexity for restricted classes of parsing models

Relation between the weak itinerant magnetism in A2A_2Ni7_7 compounds (AA = Y, La) and their stacked crystal structures

The weak itinerant magnetic properties of $A_2$Ni$_7$ compounds with $A$ = {Y, La} have been investigated using electronic band structure calculations in the relation with their polymorphic crystal structures. These compounds crystallizes in two structures resulting from the stacking of two and three blocks of [$A_2$Ni$_4$ + 2 $A$Ni$_5$] units for hexagonal $2H$-La$_2$Ni$_7$ (Ce$_2$Ni$_7$ type) and rhombohedral $3R$-Y$_2$Ni$_7$ (Gd$_2$Co$_7$ type) respectively. Experimentally, $2H$-La$_2$Ni$_7$ is a weak itinerant antiferromagnet whereas $3R$-Y$_2$Ni$_7$ is a weak itinerant ferromagnet. From the present first principles calculation within non-spin polarized state, both compounds present an electronic density of state with a sharp and narrow peak centered at the Fermi level corresponding to flat bands from $3d$-Ni. This induces a magnetic instability and both compounds are more stable in a ferromagnetic (FM) order compared to a paramagnetic state ($\Delta E \simeq$ -35 meV/f.u.). The magnetic moment of each of the five Ni sites varies with their positions relative to the [$A_2$Ni$_4$] and [$A$Ni$_5$] units: they are minimum in the [$A_2$Ni$_4$] unit and maximum at the interface between two [$A$Ni$_5$] units. For $2H$-La$_2$Ni$_7$, an antiferromagnetic (AFM) structure has been proposed and found with an energy comparable to that of the FM state. This AFM structure is described by two FM unit blocks of opposite Ni spin sign separated by a non-magnetic layer at z = 0 and $\frac12$. The Ni ($2a$) atoms belonging to this intermediate layer are located in the [La$_2$Ni$_4$] unit and are at a center of symmetry of the hexagonal cell ($P6_3/mmc$) where the resultant molecular field is cancelled. Further non-collinear spin calculations have been performed to determine the Ni moment orientations which are found preferentially parallel to the $c$ axis for both FM and AFM structures.Comment: 19 pages, 7 figures, 2 table