Discrete Projection Research Articles

The rodent medial prefrontal cortex and associated circuits in orchestrating adaptive behavior under variable demands

Emerging evidence implicates rodent medial prefrontal cortex (mPFC) in tasks requiring adaptation of behavior to changing information from external and internal sources. However, the computations within mPFC and subsequent outputs that determine behavior are incompletely understood. We review the involvement of mPFC subregions, and their projections to the striatum and amygdala in two broad types of tasks in rodents: 1) appetitive and aversive Pavlovian and operant conditioning tasks that engage mPFC-striatum and mPFC-amygdala circuits, and 2) foraging-based tasks that require decision making to optimize reward. We find support for region-specific function of the mPFC, with dorsal mPFC and its projections to the dorsomedial striatum supporting action control with higher cognitive demands, and ventral mPFC engagement in translating affective signals into behavior via discrete projections to the ventral striatum and amygdala. However, we also propose that defined mPFC subdivisions operate as a functional continuum rather than segregated functional units, with crosstalk that allows distinct subregion-specific inputs (e.g., internal, affective) to influence adaptive behavior supported by other subregions.

Smoothing a reference pathway based on discrete exogenous projections

In integrated assessment studies and scenario analysis, typically we need to calibrate a model to follow an exogenous pathway, e.g., the shared socioeconomic pathways. In these exogenous pathways, the data of key variables such as GDP and energy consumption are typically provided every five or ten years. In some cases, we need a yearly smooth pathway that is consistent with such an exogenous pathway with data of only every five years. Hence, this piece of study provides a method to obtain a smooth yearly pathway based on exogenous data of limited years.•An approach to smoothing time series of discrete variables is provided•An example is used to illustrate the approach based on the data in World Energy Outlook 2019

Statistical learning for fluid flows: Sparse Fourier divergence-free approximations

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L2 projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. In the Fourier setting, the incompressibility (divergence-free) constraint becomes a finite set of linear algebraic equations. We couple our spatial approximation with the truncated singular-value decomposition of the flow measurements for temporal compression. Our computational framework thus combines supervised and unsupervised learning techniques. We assess the capabilities of our method in various numerical examples arising in fluid mechanics.

Plemelj projections in discrete quaternionic analysis

The discrete quaternionic analysis has been placed recently in the same framework as its continuous counterpart. To discover more similarities, we study the solvability of the Dirichlet problem for discrete Cauchy–Fueter system. A serious difficulty arises due to the absence of the notion of the non-tangential limit on lattices. To overcome it, we introduce the two layered structure of discrete boundaries. It turns out that the restriction of the discrete Cauchy–Bitsadze integral on the inner layer of the discrete boundary plays the same role as the non-tangential limit of its continuous counterpart from the inside of the domain, and the analogous result holds true for the outer layer. Moreover, the discrete Sokhotski–Plemelj formula is established over an arbitrary bounded boundary. This allows us to give a criterion for the solvability of the Dirichlet problem via discrete Plemelj projections. More remarkably, we can show that the scaling limits of discrete Plemelj projections are the continuous ones. Our crucial tool is the asymptotic expansion of the fundamental solution of the discrete Cauchy–Fueter operator, instead of the classical method by V. Thomee.

Boundary Ghosts for Discrete Tomography

Discrete tomography reconstructs an image of an object on a grid from its discrete projections along relatively few directions. When the resulting system of linear equations is under-determined, the reconstructed image is not unique. Ghosts are arrays of signed pixels that have zero sum projections along these directions; they define the image pixel locations that have non-unique solutions. In general, the discrete projection directions are chosen to define a ghost that has minimal impact on the reconstructed image. Here we construct binary boundary ghosts, which only affect a thin string of pixels distant from the object centre. This means that a large portion of the object around its centre can be uniquely reconstructed. We construct these boundary ghosts from maximal primitive ghosts, configurations of $$2^N$$ connected binary ( $$\pm 1$$ ) points over N directions. Maximal ghosts obfuscate image reconstruction and find application in secure storage of digital data.

Discrete Projections: A Step Towards Particle Methods on Bounded Domains without Remeshing

We propose a simple tweak to a recently developed regularisation scheme for particle methods. This allows us to chose the particle spacing $h$ proportional to the regularisation length $\sigma$ and achieve optimal error bounds of the form $\mathcal{O}(\sigma^n)$, $n\in\mathbb{N}$, without any need of remeshing. We prove this result for the linear advection equation but also carry out high-order experiments on the full Navier--Stokes equations. In our experiments the particle methods proved to be highly accurate, long-term stable, and competitive with discontinuous Galerkin methods.

On static and free vibration analysis of FGM plates using an efficient quadrilateral finite element based on DSPM

In the present paper, a shear-locking free quadrilateral element with 5 DOFs per node, called Q4γs, is developed using a discrete shear projection method (DSPM). Independent transverse shear strains are formulated using a tangential coordinate system, and discrete shear strains are applied along each of element sides to get the constant shear strains. These constant independent transverse shear strains are projected onto each corner node, and the cartesian shear strain components are interpolated over the element domain with standard bilinear shape functions. The applications of the element in static and free vibration analysis of functionally graded material plates show good convergence behavior, high reliability, and accuracy.

Discrete projection methods for Hammerstein integral equations on the half-line

In this paper, we study discrete projection methods for solving the Hammerstein integral equations on the half-line with a smooth kernel using piecewise polynomial basis functions. We show that discrete Galerkin/discrete collocation methods converge to the exact solution with order $${\mathcal {O}}(n^{-min\{r, d\}}),$$ whereas iterated discrete Galerkin/iterated discrete collocation methods converge to the exact solution with order $${\mathcal {O}}(n^{-min\{2r, d\}}),$$ where $$n^{-1}$$ is the maximum norm of the graded mesh and r denotes the order of the piecewise polynomial employed and $$d-1$$ is the degree of precision of quadrature formula. We also show that iterated discrete multi-Galerkin/iterated discrete multi-collocation methods converge to the exact solution with order $${\mathcal {O}}(n^{-min\{4r, d\}})$$ . Hence by choosing sufficiently accurate numerical quadrature rule, we show that the convergence rates in discrete projection and discrete multi-projection methods are preserved. Numerical examples are given to uphold the theoretical results.

Shape circularity assisted tomography reconstruction

This paper deals with the binary tomography reconstruction problem for very limited projection data availability. The connection between discrete geometrical moments and orthogonal projection data is thoroughly analyzed. The circularity shape descriptor, which can be expressed by geometrical moments, is taken as a new regularization factor in the reconstruction process. A new gradient based reconstruction method is designed to incorporate this regularization. Experimental evaluation shows that the proposed method is very competitive in comparison with other recently suggested methods for limited projection availability: one or two projection directions only. The proposed approach can be a valuable tool in situations of sharply reduced projection availability.

Palmoplantar hyperkeratotic projections

Palmoplantar hyperkeratotic projections

The chronicles of coronaviruses: the electron microscope, the doughnut, and the spike

The advancement of medicine owes in large measure to a German engineer Ernst Ruska, whose invention of transmission electron microscope in 1931 won him the 1986 Nobel Prize in Physics, when it comes to infectious diseases. Encouraged by his physician brother Helmut Ruska to use the prototype instrument for the study of viruses, the course of virology was shifted to a different and unprecedented level. Virus could then be seen, identified and imaged. The University of Maryland happened to acquire an American model of transmission EM, the RCA EMU, using which the first structural study was done for the first known coronavirus (then was simply known as infectious bronchitis virus) in 1948. The virus was described as rounded bodies with filamentous projections. The magnification was not great and the resolution was poor. The study was followed by a series of studies using improved techniques and better EM spanning the next decade. An upgraded version RCA-EMU2A gave better images in 1957 and the virus was described as doughnut-like structure. Using Siemens Elmiskop, D.M. Berry and collaborators made the first high-resolution pictures in 1964. The thick envelope which gave doughnut-like appearance and filamentous projections reported before could be discerned as discrete pear-shaped projections called the spikes. These spikes form a corona-like halo around the virus, which were also seen in novel human viruses (B814 and 229E) that caused common colds. The discoverer of B814, David Tyrrell and his aid June Almeida, a magnificent electron microscopist, established that IBV, B814 and 229E were of the same kind of virus in 1967, which prompted to create the name coronavirus in 1968. This article further highlights the detail structural organisation of coronaviruses emanating from these pioneering research.

Sedimentation of general shaped particles using a multigrid fictitious boundary method

In this paper, a direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FBM), is used to simulate fluid–solid two-phase flows of different general shaped particles. The momentum interactions between solid and fluid phases are handled by using the FBM. The continuity and momentum equations are solved on a fixed Eulerian grid that is independent of flow features by using a discrete projection scheme inside a multi-grid finite element approach. A detailed description is presented for the geometric representation and modeling of two-dimensional particles of different general shapes, i.e., circular, elliptical, square, rectangular, triangular, and pentagonal shapes inside the fluid. We discussed the effects of particle shapes and the influences on the settling behavior of the particles. A comparison of the settling trajectories of the particles of the same mass but with different shapes is presented. Moreover, depending upon the particle’s shape, some interesting facts are discovered, which have a great influence on the particles’ trajectory and settling velocity. Some very important correlations between the drag force coefficient and particle’s Reynolds numbers with different density ratios of particles are obtained. Furthermore, we also studied the settling behavior of elliptical and rectangular particles with different axis ratios and a boomerang particle with different concave angles. The authors of the article agree to the retraction of the article effective AUGUST 20, 2021.

A discrete projection analogue to Pick’s theorem

Pick’s theorem expresses the area of a polygon on a grid in terms of the number of boundary and interior integer lattice points. Here, we present an analogous theorem for the area of a symmetric, convex polygon in terms of the number of polygon edges and total projection bins. These polygons arise naturally through discrete projection ghosts. Ghosts are geometric objects that define locations in discrete tomographic systems which are not uniquely determinable. In this work, we show that the area A of a ghost’s convex hull is related to the number of non-trivial discrete projection bins B over the ghost image for any set of N 2D discrete projections by A=B/2−N/2. The ratio B/A has a strong upper bound of exactly 2. This relation is analogous to Pick’s theorem for polygons with lattice point vertices.

On computer modelling of operations, geometric characteristics and methods of pulsed optical tomography of nuclear fuel microobjects

The paper refers to the area of morphological processing of projection images and its goal is to design some computer models of basic operations, geometric properties and methods of pulsed optical tomography which provide a high-speed production operational control and sorting of each microobjet (MO) of nuclear fuel in their flow according to their size and shape. Based on the proposed computer models, a precision laser method of industrial differential control and quality control of an MO flow of nuclear fuel was developed and experimentally tested. The method uses the statistical reconstruction of the size (D) and shape (K) of each microobject and takes into account the overall dimensions of the outlines of three mutually orthogonal two-dimensional pulsed discrete projection images of a microobject. The processing speed of this method is 100 MO/s in the diameter range of 400–1500 µm. The relative error of an MO diameter control is no more than 0.25% (at the reliability of PD = 0.7 and K = 1.3 relative units), and the relative error of the non-sphericity coefficient control lies in the range of 2.3% (PK = 0.7 and K = 1.3) to 0.6% (PK = 0.96 and K = 1.05).

A consistent projection finite element method for the incompressible MHD equations

ABSTRACT In this paper, we introduce a consistent projection finite element method for the impressible MHD (MagnetoHydroDynamics) equations. It's a fully discrete projection method, which associates the virtues of both the gauge and Uzawa methods with a variational framework. We also testify the unconditional stability and error estimates of the velocity, pressure and magnetic field by the variational method using some assumptions. Finally, we present some numerical experiments to support the validity of the consistent projection finite element method.

Anatomically realistic lumen motion representation in patient-specific space–time isogeometric flow analysis of coronary arteries with time-dependent medical-image data

Patient-specific computational flow analysis of coronary arteries with time-dependent medical-image data can provide valuable information to doctors making treatment decisions. Reliable computational analysis requires a good core method, high-fidelity space and time discretizations, and an anatomically realistic representation of the lumen motion. The space–time variational multiscale (ST-VMS) method has a good track record as a core method. The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the artery. The moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces. The ST isogeometric analysis is a superior discretization method. With IGA basis functions in space, it enables more accurate representation of the lumen geometry and increased accuracy in the flow solution. With IGA basis functions in time, it enables a smoother representation of the lumen motion and a mesh motion consistent with that. With cubic NURBS in time, we obtain a continuous acceleration from the lumen-motion representation. Here we focus on making the lumen-motion representation anatomically realistic. We present a method to obtain from medical-image data in discrete form an anatomically realistic NURBS representation of the lumen motion, without sudden, unrealistic changes introduced by the higher-order representation. In the discrete projection from the medical-image data to the NURBS representation, we supplement the least-squares terms with two penalty terms, corresponding to the first and second time derivatives of the control-point trajectories. The penalty terms help us avoid the sudden unrealistic changes. The computation we present demonstrates the effectiveness of the method.

Modulation of extrasynaptic GABAA alpha 5 receptors in the ventral hippocampus normalizes physiological and behavioral deficits in a circuit specific manner

Hippocampal hyperactivity is correlated with psychosis in schizophrenia patients and likely attributable to deficits in GABAergic signaling. Here we attempt to reverse this deficit by overexpression of the α5-GABAA receptor within the ventral hippocampus (vHipp). Indeed, this is sufficient to normalize vHipp activity and downstream alterations in dopamine neuron function in the MAM rodent model. This approach also attenuated behavioral deficits in cognitive flexibility. To understand the specific pathways that mediate these effects, we used chemogenetics to manipulate discrete projections from the vHipp to the nucleus accumbens (NAc) or prefrontal cortex (mPFC). We found that inhibition of the vHipp-NAc, but not the vHipp-mPFC pathway, normalized aberrant dopamine neuron activity. Conversely, inhibition of the vHipp-mPFC improved cognitive function. Taken together, these results demonstrate that restoring GABAergic signaling in the vHipp improves schizophrenia-like deficits and that distinct behavioral alterations are mediated by discrete projections from the vHipp to the NAc and mPFC.

SUN-473 The Contribution of Bmal1 Expression in the Suprachiasmatic Nucleus to Female Fertility

The preovulatory gonadotropin-releasing hormone (GnRH) and resulting luteinizing hormone (LH) surge is gated to the onset of the active period in mice by a circadian and steroid signal. The temporal signal that initiates this process is believed to arrive from the suprachiasmatic nucleus (SCN), the hypothalamic circadian pacemaker. The SCN may contribute to reproduction through two discrete projections: vasoactive inhibitory peptide (VIP) neurons in the SCN project to gonadotropin-releasing hormone (GnRH) neurons in the preoptic area, and arginine vasopressin (AVP) neurons in the SCN project to kisspeptin (Kiss1) neurons in the anteroventral periventricular (AVPV). Genomic deletion of the critical circadian clock component, Bmal1, results in infertility in females. We sought to determine whether Bmal1 was critical in the SCN VIP and AVP neurons by using cre/lox technology to create three lines of mutant mice: AVP-Bmal1-/-, VIP-Bmal1-/-, and AVP-VIP-Bmal1-/-. We found no significant difference in LH levels following a kisspeptin challenge (2 mg/kg) between AVP-Bmal1-/- and Bmal1flox/flox (617.4 ± 216.9 vs 629.6 ± 110.6 pg/mL) or GnRH challenge (10 μg/kg) (1029.0 ± 246.2 vs 712.7 ± 142.6 pg/mL). Preliminary findings of an induced LH surge found AVP-Bmal1-/- and VIP-Bmal1-/- mice are able to mount a surge at the time of lights off (Bmal1flox/flox: 3 of 5; AVP-Bmal1-/-: 1 of 2, VIP-Bmal1:-/- 4 of 4; AVP-VIP-Bmal1-/- 0 of 2). Additionally, we were able to detect an endogenous surge at the time of lights off in both AVP-Bmal1-/-, VIP-Bmal1-/- mice, but not AVP-VIP-Bmal1-/-. However, AVP-Bmal1-/-, VIP-Bmal1-/-, and AVP-VIP-Bmal1-/- females carried litters to term and show no differences in the time to first litter compared to Bmal1flox/flox control (AVP-Bmal1-/-: 48 ± 4.8 vs 44.3 ± 0.3 days; VIP-Bmal1-/-: 29.6 ± 7.7 vs 31.0 ± 4.2 days; AVP-VIP-Bmal1-/-;27.7 ± 7 vs 23 ± 0 days); number of litters in 100 days (AVP-Bmal1-/-: 3.7 ±0.6 vs 4 ± 0.6; VIP-Bmal1-/-: 3.0 ± 1.0 vs 3.0 ± 0.0; AVP-VIP-Bmal1-/- 3.5 ± 0.7 vs 3.5 ± 0.7 days); or pups per litter (AVP-Bmal1-/-: 7.2 ± 0.7 vs 7.3 ± 0.7; VIP-Bmal1-/-: 6.2 ± 1.6 vs 7.6 ± 2.9; AVP-VIP-Bmal1-/- 8.1 ± 0.9 vs 9 ± 1.4 pups). Overall, these findings suggest that Bmal1 expression in the SCN AVP or VIP neurons is not required for fertility in a 12:12 light:dark cycle.

An incremental pressure correction finite element method for the time-dependent Oldroyd flows

In this paper, we present an incremental pressure correction finite element method for the time-dependent Oldroyd flows. This method is a fully discrete projection method. As we all know, most projection methods have been studied without space discretization. Then the ensuing analysis may not extend to this case. We also give the stability analysis and the optimal error analysis. The analysis is based on a time discrete error and a spatial discrete error. In order to show the effectiveness of the method, we also present some numerical results. The numerical results confirm our analysis and show clearly the stability and optimal convergence of the incremental pressure correction finite element method for the time-dependent Oldroyd flows.

Neurod1 Is Essential for the Primary Tonotopic Organization and Related Auditory Information Processing in the Midbrain.

Hearing depends on extracting frequency, intensity, and temporal properties from sound to generate an auditory map for acoustical signal processing. How physiology intersects with molecular specification to fine tune the developing properties of the auditory system that enable these aspects remains unclear. We made a novel conditional deletion model that eliminates the transcription factor NEUROD1 exclusively in the ear. These mice (both sexes) develop a truncated frequency range with no neuroanatomically recognizable mapping of spiral ganglion neurons onto distinct locations in the cochlea nor a cochleotopic map presenting topographically discrete projections to the cochlear nuclei. The disorganized primary cochleotopic map alters tuning properties of the inferior colliculus units, which display abnormal frequency, intensity, and temporal sound coding. At the behavioral level, animals show alterations in the acoustic startle response, consistent with altered neuroanatomical and physiological properties. We demonstrate that absence of the primary afferent topology during embryonic development leads to dysfunctional tonotopy of the auditory system. Such effects have never been investigated in other sensory systems because of the lack of comparable single gene mutation models.SIGNIFICANCE STATEMENT All sensory systems form a topographical map of neuronal projections from peripheral sensory organs to the brain. Neuronal projections in the auditory pathway are cochleotopically organized, providing a tonotopic map of sound frequencies. Primary sensory maps typically arise by molecular cues, requiring physiological refinements. Past work has demonstrated physiologic plasticity in many senses without ever molecularly undoing the specific mapping of an entire primary sensory projection. We genetically manipulated primary auditory neurons to generate a scrambled cochleotopic projection. Eliminating tonotopic representation to auditory nuclei demonstrates the inability of physiological processes to restore a tonotopic presentation of sound in the midbrain. Our data provide the first insights into the limits of physiology-mediated brainstem plasticity during the development of the auditory system.