Sharing storage using dirty vectors

Consider a computation F with n inputs (independent variables) and m outputs (dependent variables) and suppose that we wish to evaluate the Jacobian of F. Automatic differentiation commonly performs this evaluation by associating vector storage either with the program variables (in the case of forward-mode automatic differentiation) or with the adjoint variables (in the case of reverse). Each vector component contains a partial derivative with respect to an independent variable, or a partial derivative of a dependent variable, respectively. The vectors may be full vectors, or they may be dynamically managed sparse data structures. In either case, many of these vectors will be scalar multiples of one another. For example, any intermediate variable produced by a unary operation in the forward mode will have a derivative vector that is a multiple of the derivative for the argument. Any computational graph node that is read just once during its lifetime will have an adjoint vector that is a multiple of the adjoint of the node that reads it. It is frequently wasteful to perform component multiplications explicitly. A scalar multiple of another vector can be replaced by a single multiplicative "scale factor" together with a pointer to the other vector. Automated use of this "dirty vector" technique can save considerable memory management overhead and dramatically reduce the number of floating-point operations required. In particular, dirty vectors often allow shared threads of computation to be reverse-accumulated cheaply. The mechanism permits a number of generalizations, some of which give efficient techniques for preaccumulation

Quantum ergodicity for restrictions to hypersurfaces

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.Comment: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearit

Antiferromagnetic ordering and dipolar interactions of YbAlO3_3

In this paper we report low-temperature magnetic properties of the rare-earth perovskite material YbAlO$_3$. Results of elastic and inelastic neutron scattering experiment, magnetization measurements along with the crystalline electrical field (CEF) calculations suggest that the ground state of Yb moments is a strongly anisotropic Kramers doublet, and the moments are confined in the $ab$-plane, pointing at an angle of $\varphi = \pm 23.5^{\circ}$ to the $a$-axis. With temperature decreasing below $T_{\rm N}=0.88$ K, Yb moments order into the coplanar, but non-collinear antiferromagnetic (AFM) structure $AxGy$, where the moments are pointed along their easy-axes. In addition, we highlight the importance of the dipole-dipole interaction, which selects the type of magnetic ordering and may be crucial for understanding magnetic properties of other rare-earth orthorhombic perovskites. Further analysis of the broad diffuse neutron scattering shows that one-dimensional interaction along the $c$-axis is dominant, and suggests YbAlO$_3$ as a new member of one dimensional quantum magnets.Comment: 8 pages, 6 figure

Competition and coexistence of antiferromagnetism and superconductivity in underdoped Ba(Fe0.953Co0.047)2As2

Neutron and x-ray diffraction studies show that the simultaneous first-order transition to an orthorhombic and antiferromagnetic (AFM) ordered state in BaFe2As2 splits into two transitions with Co doping. For Ba(Fe0.953Co0.047)2As2, a tetragonal-orthorhombic transition occurs at TS = 60 K, followed by a second-order transition to AFM order at TN = 47 K. Superconductivity (SC) occurs in the orthorhombic state below TC = 15 K and coexists with AFM. Below TC, the static Fe moment is reduced and a 4 meV spin gap develops indicating competition between coexisting SC and AFM order.Comment: 15 pages, 4 figure

Congenital anomalies in black South African liveborn neonates at an urban academic hospital

Study objective. The aim was to study the spectrum of clinical problems and outcomes in infants born at an urban academic hospital. In consequence, as part of the overall study, the incidence of congenital anomalies and the outcomes of affected infants were recorded.Design. This was a prospective, hospital-based study, undertaken on liveborn infants born over a 3-year period, 1 May 1986 to 30 April 1989.Setting. Kalafong Hospital, Pretoria.Main results. A total of 17 351 liveborn infants was examined and the total congenital anomalies incidence was 11 ,87 per 1 000 Iivebirths. The central nervous system was the system most frequently involved (2,30 per 1 000 livebirths), followed by the musculoskeletal system (2,13 per 1 000 livebirths). The commonest individual congenital anomaly was Down syndrome (1,33 per 1 000 Iivebirths), followed by neural tube defects (0,99 per 1 000 livebirths) and ventricular septal defects (0,69 per 1 000 livebirths). In 11 % (2,25 per 1 000 livebirths) of neonatal deaths, infant loss was attributable to congenital anomalies.Conclusions. The incidence of congenital anomalies in black South African neonates, born in an urban setting, is as high as in other First- and Third-World countries, and the incidence of some individual congenital anomalies is higher. This study indicates the need for further research and the establishment of prenatal, genetics and paediatric facilities to manage these problems

Reduced Polymorphism Associated with X Chromosome Meiotic Drive in the Stalk-Eyed Fly Teleopsis dalmanni

Sex chromosome meiotic drive has been suggested as a cause of several evolutionary genetic phenomena, including genomic conflicts that give rise to reproductive isolation between new species. In this paper we present a population genetic analysis of X chromosome drive in the stalk-eyed fly, Teleopsis dalmanni, to determine how this natural polymorphism influences genetic diversity. We analyzed patterns of DNA sequence variation at two X-linked regions (comprising 1325 bp) approximately 50 cM apart and one autosomal region (comprising 921 bp) for 50 males, half of which were collected in the field from one of two allopatric locations and the other half were derived from lab-reared individuals with known brood sex ratios. These two populations are recently diverged but exhibit partial postzygotic reproductive isolation, i.e. crosses produce sterile hybrid males and fertile females. We find no nucleotide or microsatellite variation on the drive X chromosome, whereas the same individuals show levels of variation at autosomal regions that are similar to field-collected flies. Furthermore, one field-caught individual collected 10 years previously had a nearly identical X haplotype to the drive X, and is over 2% divergent from other haplotypes sampled from the field. These results are consistent with a selective sweep that has removed genetic variation from much of the drive X chromosome. We discuss how this finding may relate to the rapid evolution of postzygotic reproductive isolation that has been documented for these flies