MP-CE Method for Space-Filling Design in Constrained Space with Multiple Types of Factors

Space-filling design selects points uniformly in the experimental space, bringing considerable flexibility to the complex-model-based and model-free data analysis. At present, space-filling designs mostly focus on regular spaces and continuous factors, with a lack of studies into the discrete factors and the constraints among factors. Most of the existing experimental design methods for qualitative factors are not applicable for discrete factors, since they ignore the potential order or spatial distance between discrete factors. This paper proposes a space-filling method, called maximum projection coordinate-exchange (MP-CE), taking into account both the diversity of factor types and the complexity of factor constraints. Specifically, the maximum projection criterion and distance criterion are introduced to capture the “bad” coordinates, and the coordinate-exchange and the optimization of experimental design are realized by solving one-dimensional constrained optimization problem. Meanwhile, by adding iterative perturbations to the traditional coordinate exchange process, the adjacent areas of the local optimal solution are explored and the optimum performances of the current optimal solution are retained, while the shortcomings of random restart are effectively avoided. Experiments in the regular space and constraint space, as well as experimental design for the terminal interception effectiveness of a missile defense system, show that the MP-CE method significantly outperforms existing popular space-filling design methods in terms of space-projection properties, while yielding comparable or superior space-filling properties.

Epigenomic diversity of cortical projection neurons in the mouse brain

Neuronal cell types are classically defined by their molecular properties, anatomy and functions. Although recent advances in single-cell genomics have led to high-resolution molecular characterization of cell type diversity in the brain1, neuronal cell types are often studied out of the context of their anatomical properties. To improve our understanding of the relationship between molecular and anatomical features that define cortical neurons, here we combined retrograde labelling with single-nucleus DNA methylation sequencing to link neural epigenomic properties to projections. We examined 11,827 single neocortical neurons from 63 cortico-cortical and cortico-subcortical long-distance projections. Our results showed unique epigenetic signatures of projection neurons that correspond to their laminar and regional location and projection patterns. On the basis of their epigenomes, intra-telencephalic cells that project to different cortical targets could be further distinguished, and some layer 5 neurons that project to extra-telencephalic targets (L5 ET) formed separate clusters that aligned with their axonal projections. Such separation varied between cortical areas, which suggests that there are area-specific differences in L5 ET subtypes, which were further validated by anatomical studies. Notably, a population of cortico-cortical projection neurons clustered with L5 ET rather than intra-telencephalic neurons, which suggests that a population of L5 ET cortical neurons projects to both targets. We verified the existence of these neurons by dual retrograde labelling and anterograde tracing of cortico-cortical projection neurons, which revealed axon terminals in extra-telencephalic targets including the thalamus, superior colliculus and pons. These findings highlight the power of single-cell epigenomic approaches to connect the molecular properties of neurons with their anatomical and projection properties.

Spatially patterned excitatory neuron subtypes and projections of the claustrum

The claustrum is a functionally and structurally complex brain region, whose very spatial extent remains debated. Histochemical-based approaches typically treat the claustrum as a relatively narrow anatomical region that primarily projects to the neocortex, whereas circuit-based approaches can suggest a broader claustrum region containing projections to the neocortex and other regions. Here, in the mouse, we took a bottom-up and cell-type-specific approach to complement and possibly unite these seemingly disparate conclusions. Using single-cell RNA-sequencing, we found that the claustrum comprises two excitatory neuron subtypes that are differentiable from the surrounding cortex. Multicolor retrograde tracing in conjunction with 12-channel multiplexed in situ hybridization revealed a core-shell spatial arrangement of these subtypes, as well as differential downstream targets. Thus, the claustrum comprises excitatory neuron subtypes with distinct molecular and projection properties, whose spatial patterns reflect the narrower and broader claustral extents debated in previous research. This subtype-specific heterogeneity likely shapes the functional complexity of the claustrum.

Calibration Method for Central Catadioptric Camera Using Multiple Groups of Parallel Lines and Their Properties

This paper presents an approach for calibrating omnidirectional single-viewpoint sensors using the central catadioptric projection properties of parallel lines. Single-viewpoint sensors are widely used in robot navigation and driverless cars; thus, a high degree of calibration accuracy is needed. In the unit viewing sphere model of central catadioptric cameras, a line in a three-dimensional space is projected to a great circle, resulting in the projections of a group of parallel lines intersecting only at the endpoints of the diameter of the great circle. Based on this property, when there are multiple groups of parallel lines, a group of orthogonal directions can be determined by a rectangle constructed by two groups of parallel lines in different directions. When there is a single group of parallel lines in space, the diameter and tangents at their endpoints determine a group of orthogonal directions for the plane containing the great circle. The intrinsic parameters of the camera can be obtained from the orthogonal vanishing points in the central catadioptric image plane. An optimization algorithm for line image fitting based on the properties of antipodal points is proposed. The performance of the algorithm is verified using simulated setups. Our calibration method was validated though simulations and real experiments with a catadioptric camera.

Equidistant, Standard and Secant Parallels

The paper describes a study of equidistant, standard and secant parallels in normal aspect cylindrical and conical projections. First, the explanation of cylindrical and conical projections as projections on cylindrical or conical surfaces is not recommended because it leads to misunderstanding projection properties. Furthermore, equidistant, standard and secant parallels are often assumed to be identical in references. After defining these three types of parallels, it is proved that it is necessary to differentiate them in the theory of map projections and teaching it.

Epigenomic Diversity of Cortical Projection Neurons in the Mouse Brain

SummaryNeuronal cell types are classically defined by their molecular properties, anatomy, and functions. While recent advances in single-cell genomics have led to high-resolution molecular characterization of cell type diversity in the brain, neuronal cell types are often studied out of the context of their anatomical properties. To better understand the relationship between molecular and anatomical features defining cortical neurons, we combined retrograde labeling with single-nucleus DNA methylation sequencing to link epigenomic properties of cell types to neuronal projections. We examined 11,827 single neocortical neurons from 63 cortico-cortical (CC) and cortico-subcortical long-distance projections. Our results revealed unique epigenetic signatures of projection neurons that correspond to their laminar and regional location and projection patterns. Based on their epigenomes, intra-telencephalic (IT) cells projecting to different cortical targets could be further distinguished, and some layer 5 neurons projecting to extra-telencephalic targets (L5-ET) formed separate subclusters that aligned with their axonal projections. Such separation varied between cortical areas, suggesting area-specific differences in L5-ET subtypes, which were further validated by anatomical studies. Interestingly, a population of CC projection neurons clustered with L5-ET rather than IT neurons, suggesting a population of L5-ET cortical neurons projecting to both targets (L5-ET+CC). We verified the existence of these neurons by labeling the axon terminals of CC projection neurons and observed clear labeling in ET targets including thalamus, superior colliculus, and pons. These findings highlight the power of single-cell epigenomic approaches to connect the molecular properties of neurons with their anatomical and projection properties.

MODELLING SOCIO-ECONOMIC DIFFERENCES IN MORTALITY USING A NEW AFFLUENCE INDEX

We introduce a new modelling framework to explain socio-economic differences in mortality in terms of an affluence index that combines information on individual wealth and income. The model is illustrated using data on older Danish males over the period 1985–2012 reported in the Statistics Denmark national register database. The model fits the historical mortality data well, captures their key features, generates smoothed death rates that allow us to work with a larger number of sub-groups than has previously been considered feasible, and has plausible projection properties.