On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

The effect of projections on dimension in the Heisenberg group

We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.

Correlation between broiler lameness and anatomical measurements of bone using radiographical projections with assessments of consistency across and within radiographs.

Lameness represents a major welfare and production issue in the poultry industry with a recent survey estimating 27% of birds lame and 3% unable to walk by 40 d of age. A variety of factors may induce lameness and are typically grouped into 2 broad classes on the basis of being infectious or skeletal in nature with the latter accounting for the majority of cases. The current work sought to build upon a large body of literature assessing the anatomical properties of bone in lame birds. Our specific objectives sought to identify relationships between relevant anatomical properties of the tibia and metatarsus using digital quantification from radiographs of legs and a measure of walking difficulty. Resulting output was statistically analyzed to assess 1) observer reliability for consistency in placing the leg during the radiograph procedure and quantification of the various measures within a radiograph, 2) the relationship between the various measurements of anatomical bone properties and sex, bird mass, and gait score, and 3) the relationship between each measurement and leg symmetry. Our anatomical bone measures were found to be reliable (intra-rater and test-retest reliabilities < 0.75) within radiograph for all measures and 8 of the 10 measures across radiographs. Several measures of bone properties in the tibia correlated to difficulty walking as measured by gait score (P < 0.05), indicating greater angulations with increasing lameness. Of the measures that manifested a gait score × bird mass interaction, heavier birds appeared to exhibit less angulation with increasing difficulty walking with lighter birds the opposite. These interactions suggest possibilities for influencing effects of activity or feed intake on bone mineralization with the bone angulation observed. Our efforts agree with that of others and indicate that angulation of the tibia may be related to lameness, though subsequent efforts involving comprehensive measures of bird activity, growth rates, and internal bone structure will be needed if the validity of the measures are to be accepted.

An Ensemble Kalman Filter multi-tracer assimilation: Determining uncertain ocean model parameters for improved climate-carbon cycle projections

An Ensemble Kalman Filter is applied to assimilate observed tracer fields in various combinations in the Bern3D ocean model. Each tracer combination yields a set of optimal transport parameter values that are used in projections with prescribed CO2 stabilization pathways. The assimilation of temperature and salinity fields yields a too vigorous ventilation of the thermocline and the deep ocean, whereas the inclusion of CFC-11 and radiocarbon improves the representation of physical and biogeochemical tracers and of ventilation time scales. Projected peak uptake rates and cumulative uptake of CO2 by the ocean are around 20% lower for the parameters determined with CFC-11 and radiocarbon as additional target compared to those with salinity and temperature only. Higher surface temperature changes are simulated in the Greenland–Norwegian–Iceland Sea and in the Southern Ocean when CFC-11 is included in the Ensemble Kalman model tuning. These findings highlights the importance of ocean transport calibration for the design of near-term and long-term CO2 emission mitigation strategies and for climate projections.

Oxygen and indicators of stress for marine life in multi-model global warming projections

Decadal-to-century scale trends for a range of marine environmental variables in the upper mesopelagic layer (UML, 100–600 m) are investigated using results from seven Earth System Models forced by a high greenhouse gas emission scenario. The models as a class represent the observation-based distribution of oxygen (O2) and carbon dioxide (CO2), albeit major mismatches between observation-based and simulated values remain for individual models. By year 2100 all models project an increase in SST between 2 °C and 3 °C, and a decrease in the pH and in the saturation state of water with respect to calcium carbonate minerals in the UML. A decrease in the total ocean inventory of dissolved oxygen by 2% to 4% is projected by the range of models. Projected O2 changes in the UML show a complex pattern with both increasing and decreasing trends reflecting the subtle balance of different competing factors such as circulation, production, remineralization, and temperature changes. Projected changes in the total volume of hypoxic and suboxic waters remain relatively small in all models. A widespread increase of CO2 in the UML is projected. The median of the CO2 distribution between 100 and 600m shifts from 0.1–0.2 mol m−3 in year 1990 to 0.2–0.4 mol m−3 in year 2100, primarily as a result of the invasion of anthropogenic carbon from the atmosphere. The co-occurrence of changes in a range of environmental variables indicates the need to further investigate their synergistic impacts on marine ecosystems and Earth System feedbacks.

Polysensory interneuronal projections to foot contractile pedal neurons in Hermissenda.

A Pavlovian-conditioning procedure may produce modifications in multiple behavioral responses. As an example, conditioning may result in the elicitation of a specific somatomotor conditioned response (CR) and, in addition, other motor and visceral CRs. In the mollusk Hermissenda conditioning produces two conditioned responses: foot-shortening and decreased locomotion. The neural circuitry supporting ciliary locomotion is well characterized, although the neural circuit underlying foot-shortening is poorly understood. Here we describe efferent neurons in the pedal ganglion that produce contraction or extension of specific regions of the foot in semi-intact preparations. Synaptic connections between polysensory type Ib and type Is interneurons and identified foot contractile efferent neurons were examined. Type Ib and type Is interneurons receive synaptic input from the visual, graviceptive, and somatosensory systems. Depolarization of type Ib interneurons evoked spikes in identified tail and lateral foot contractile efferent neurons. Mechanical displacement of the statocyst evoked complex excitatory postsynaptic potentials (EPSPs) and spikes recorded from type Ib and type Is interneurons and complex EPSPs and spikes in identified foot contractile efferent neurons. Depolarization of type Ib interneurons in semi-intact preparations produced contraction and shortening along the rostrocaudal axis of the foot. Depolarization of Is interneurons in semi-intact preparations produced contraction of the anterior region of the foot. Taken collectively, the results suggest that type Ib and type Is polysensory interneurons may contribute to the neural circuit underlying the foot-shortening CR in Hermissenda.

Dominance of the proximal coordinate frame in determining the locations of hippocampal place cell activity during navigation.

The place-specific activity of hippocampal cells provides downstream structures with information regarding an animal's position within an environment and, perhaps, the location of goals within that environment. In rodents, recent research has suggested that distal cues primarily set the orientation of the spatial representation, whereas the boundaries of the behavioral apparatus determine the locations of place activity. The current study was designed to address possible biases in some previous research that may have minimized the likelihood of observing place activity bound to distal cues. Hippocampal single-unit activity was recorded from six freely moving rats as they were trained to perform a tone-initiated place-preference task on an open-field platform. To investigate whether place activity was bound to the room- or platform-based coordinate frame (or both), the platform was translated within the room at an "early" and at a "late" phase of task acquisition (Shift 1 and Shift 2). At both time points, CA1 and CA3 place cells demonstrated room-associated and/or platform-associated activity, or remapped in response to the platform shift. Shift 1 revealed place activity that reflected an interaction between a dominant platform-based (proximal) coordinate frame and a weaker room-based (distal) frame because many CA1 and CA3 place fields shifted to a location intermediate to the two reference frames. Shift 2 resulted in place activity that became more strongly bound to either the platform- or room-based coordinate frame, suggesting the emergence of two independent spatial frames of reference (with many more cells participating in platform-based than in room-based representations).

Institutionalizing Intensive Family Preservation Services: A Strategy for Creating Staffing Standards Based on Projections of At-Risk Children from Referral Sources

In spite of new legislation and much public and professional interest, intensive family preservation service (IFPS) remains in a vulnerable position as compared to other child welfare services. This article details a method to project ideal IFPS caseloads as a function of children who are at-risk for placement by various referral sources. Using this approach, resource allocation for IFPS can be more nearly on equal ground with the traditional child welfare functions and help IFPS to assume its needed place as a core service in the child welfare continuum.

Analysis of the mechanisms that maintain coordinate production of $\alpha$- and $\beta$-tubulin in mammalian cells

Alpha and beta tubulin are essential proteins in all eukaryotic cells. To study how cells maintain coordinate levels of these two interacting proteins, we have used PCR to add a 9 amino acid epitope from influenza hemagglutinin protein onto the carboxyl terminus of $\alpha$1 and $\beta$1-tubulin. The chimeric tubulin genes (HA$\alpha$1 and HA$\beta$1) were transfected into CHO cells and cell lines that stably express each gene were selected. Cells transfected with HA-tubulin do not exhibit any gross changes in growth or morphology. Immunofluorescence analysis demonstrated that HA-tubulins incorporate into both cytoplasmic and spindle microtubules. A quantitative biochemical assay was used to show that HA-tubulins incorporate into microtubules to a normal extent and do not alter the steady state distribution of endogenous tubulin between monomer and polymer pools. Two-dimensional gel analysis of pulse-labeled cells indicated that when HA$\beta$1-tubulin is expressed at high levels, it slightly represses the synthesis of the endogenous $\beta$-tubulin but produces a small increase in the synthesis of $\alpha$-tubulin. Analysis of cells labeled to steady state showed that HA$\beta$1-tubulin accumulates to a similar level as the wild-type gene product, but together these polypeptides produce only a small increase in total tubulin content consistent with the increased synthesis of $\alpha$-tubulin. It thus appears that HA$\beta$1-tubulin successfully competes with endogenous $\beta$-tubulin for heterodimer formation and that free $\beta$-tubulin subunits (endogenous and HA$\beta$1) are selectively degraded to maintain coordinate amounts of $\alpha$- and $\beta$-tubulin. In addition, the increased synthesis of $\alpha$-tubulin suggested the existence of a mechanism to ensure coordinate synthesis of $\alpha$- and $\beta$-tubulin subunits. To analyze whether reciprocal changes in endogenous tubulin synthesis occur when $\alpha$-tubulin is overexpressed, stably transfected CHO cell lines were isolated in which HA$\alpha$1-tubulin represents 50% of the total $\alpha$-tubulin, and its relative abundance can be further increased to 85-90% by treatment with sodium butyrate. In contrast with results obtained using HA$\beta$1-tubulin, transfection of HA$\alpha$1-tubulin decreased the synthesis of endogenous $\alpha$-tubulin to 60% of normal with little or no change in $\beta$-tubulin synthesis. When the transfected cells were treated with sodium butyrate to further increase HA$\beta$1-tubulin production, a larger decrease in the synthesis of endogenous $\alpha$-tubulin (to 30% of normal) was observed. The repression on the synthesis of endogenous $\alpha$-tubulin polypeptide was found to be directly proportional to the expression of HA$\alpha$1-tubulin indicating the existence of an autoregulatory loop, where $\alpha$-tubulin inhibits its own synthesis. To determine whether overproduction of HA$\alpha$1-tubulin affected the transcription, message stability or translation of endogenous $\alpha$-tubulin, the steady state levels of $\alpha$-tubulin mRNA were analyzed by ribonuclease protection assays. The results showed that the steady state level of $\alpha$-tubulin mRNA is not affected by the overexpression of HA$\alpha$1-tubulin, indicating that the repression is translational. The results are compatible with a model in which $\beta$-tubulin synthesis is largely unperturbed by overexpression of other tubulin subunits, and excess $\beta$-tubulin subunits are rapidly degraded to maintain coordinate $\alpha$- and $\beta$-tubulin levels at steady state. In contrast, free $\alpha$-tubulin represses its own synthesis at the translational level, suggesting that its level of production may be controlled by the amount of $\beta$-tubulin available for heterodimer formation. ^

AN ELECTROPHYSIOLOGICAL ANALYSIS OF THE AMYGDALOID AND SUBICULAR PROJECTIONS TO THE VENTROMEDIAL NUCLEUS OF THE HYPOTHALAMUS IN THE RABBIT

Electrophysiological experiments were performed on 96 male New Zealand white rabbits, anesthetized with urethane. Glass electrodes, filled with 2M NaCl, were used for microstimulation of three fiber pathways projecting from "limbic" centers to the ventromedial nucleus of the hypothalamus (VMH). Unitary and field potential recordings were made in the VMH after stimulation.^ Stimulation of the lateral portion of the fimbria, which carries fibers from the ventral subiculum of the hippocampal formation, evokes predominantly an inhibition of neurons medially in the VMH, and excitation of neurons located laterally.^ Stimulation of the dorsal portion of the stria terminalis, which carries fibers from the cortical nucleus of the amygdala, also produces predominantly an inhibition of cells medially and excitation laterally.^ Stimulation of the ventral component of the stria terminalis, which carries fibers from the medial nucleus of the amygdala, evokes excitation of cell medially, with little or no response seen laterally.^ Cells recorded medially in the VMH received convergent inputs from each of the three fiber systems: inhibition from fimbria and dorsal stria stimulation, excitation from ventral stria stimulation.^ The excitatory unitary responses recorded medially to ventral stria stimulation and laterally to fimbria and dorsal stria stimulation were subjected to a series of threshold stimulus intensities. From these tests it was determined that each of these three projections terminates monosynaptically on VMH neurons.^ The evidence for convergence upon single VMH neurons of projections from the amygdala and the hippocampal formation suggests this area of the brain to be important for integration of information from these two limbic centers. The VMH has been implied in a number of behavioral states: eating, reproduction, defense and aggression; it has further been linked to control of the anterior pituitary. These data provide a functional circuit through which the amygdaloid complex and the hippocampal formation can channel information from higher cortical centers into a hypothalamic area capable of coordinating behavioral and hormonal responses. ^

On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

On the reduced sensitivity of the Atlantic overturning to Greenland ice sheet melting in projections: a multi-model assessment

Large uncertainties exist concerning the impact of Greenland ice sheet melting on the Atlantic meridional overturning circulation (AMOC) in the future, partly due to different sensitivity of the AMOC to freshwater input in the North Atlantic among climate models. Here we analyse five projections from different coupled ocean–atmosphere models with an additional 0.1 Sv (1 Sv = 10 6 m3/s) of freshwater released around Greenland between 2050 and 2089. We find on average a further weakening of the AMOC at 26°N of 1.1 ± 0.6 Sv representing a 27 ± 14% supplementary weakening in 2080–2089, as compared to the weakening relative to 2006–2015 due to the effect of the external forcing only. This weakening is lower than what has been found with the same ensemble of models in an identical experimen - tal set-up but under recent historical climate conditions. This lower sensitivity in a warmer world is explained by two main factors. First, a tendency of decoupling is detected between the surface and the deep ocean caused by an increased thermal stratification in the North Atlantic under the effect of global warming. This induces a shoaling of ocean deep ventilation through convection hence ventilating only intermediate levels. The second important effect concerns the so-called Canary Current freshwater leakage; a process by which additionally released fresh water in the North Atlantic leaks along the Canary Current and escapes the convection zones towards the subtropical area. This leakage is increasing in a warming climate, which is a consequence of decreasing gyres asymmetry due to changes in Ekman rumping. We suggest that these modifications are related with the northward shift of the jet stream in a warmer world. For these two reasons the AMOC is less susceptible to freshwater perturbations (near the deep water formation sides) in the North Atlantic as compared to the recent historical climate conditions. Finally, we propose a bilinear model that accounts for the two former processes to give a conceptual explanation about the decreasing AMOC sensitivity due to freshwater input. Within the limit of this bilinear model, we find that 62 ± 8% of the reduction in sensitivity is related with the changes in gyre asymmetry and freshwater leakage and 38 ± 8% is due to the reduction in deep ocean ventilation associated with the increased stratification in the North Atlantic.

Percutaneous screw fixation of the iliosacral joint: optimal screw pathways are frequently not completely intraosseous

INTRODUCTION In iliosacral screw fixation, the dimensions of solely intraosseous (secure) pathways, perpendicular to the ilio-sacral articulation (optimal) with corresponding entry (EP) and aiming points (AP) on lateral fluoroscopic projections, and the factors (demographic, anatomic) influencing these have not yet been described. METHODS In 100 CTs of normal pelvises, the height and width of the secure and optimal pathways were measured on axial and coronal views bilaterally (total measurements: n=200). Corresponding EP and AP were defined as either the location of the screw head or tip at the crossing of lateral innominate bones' cortices (EP) and sacral midlines (AP) within the centre of the pathway, respectively. EP and AP were transferred to the sagittal pelvic view using a coordinate system with the zero-point in the centre of the posterior cortex of the S1 vertebral body (x-axis parallel to upper S1 endplate). Distances are expressed in relation to the anteroposterior distance of the S1 upper endplate (in %). The influence of demographic (age, gender, side) and/or anatomic (PIA=pelvic incidence angle; TCA=transversal curvature angle, PID-Index=pelvic incidence distance-index; USW=unilateral sacral width-index) parameters on pathway dimensions and positions of EP and AP were assessed (multivariate analysis). RESULTS The width, height or both factors of the pathways were at least 7mm or more in 32% and 53% or 20%, respectively. The EP was on average 14±24% behind the centre of the posterior S1 cortex and 41±14% below it. The AP was on average 53±7% in the front of the centre of the posterior S1 cortex and 11±7% above it. PIA influenced the width, TCA, PID-Index the height of the pathways. PIA, PID-Index, and USW-Index significantly influenced EP and AP. Age, gender, and TCA significantly influenced EP. CONCLUSION Secure and optimal placement of screws of at least 7mm in diameter will be unfeasible in the majority of patients. Thoughtful preoperative planning of screw placement on CT scans is advisable to identify secure pathways with an optimal direction. For this purpose, the presented methodology of determining and transferring EPs and APs of corresponding pathways to the sagittal pelvic view using a coordinate system may be useful.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.