Spatial Version Research Articles

17β-Estradiol, but not estrone, increases the survival and activation of new neurons in the hippocampus in response to spatial memory in adult female rats

Estrogens fluctuate across the lifespan in women, with circulating 17β-estradiol levels higher pre-menopause than estrone and circulating estrone levels higher postmenopause than 17β-estradiol. Estrone is a common component of hormone replacement therapies, but research shows that 17β-estradiol may have a greater positive impact on cognition. Previous studies show that acute estrone and 17β-estradiol impact hippocampus-dependent learning and cell proliferation in the dentate gyrus in a dose-dependent manner in adult female rats. The current study explores how chronic treatment with estrone and 17β-estradiol differentially influences spatial learning, hippocampal neurogenesis and activation of new neurons in response to spatial memory. Adult female rats received daily injections of vehicle (sesame oil), or a 10μg dose of either 17β-estradiol or estrone for 20days. One day following the first hormone injection all rats were injected with the DNA synthesis marker, bromodeoxyuridine. On days 11–15 after BrdU injection rats were trained on a spatial reference version of the Morris water maze, and five days later (day 20 of estrogens treatment) were given a probe trial to assess memory retention. Cell proliferation was assessed by the endogenous cell cycle marker, Ki67, cell survival was assessed by counting the number and density of BrdU-ir cells in the dentate gyrus and cell activation was assessed by the percentage of BrdU-ir cells that were co-labelled with the immediate early gene product zif268. There were no significant differences between groups in acquisition or retention of Morris water maze. However, the 17β-estradiol group had significantly higher, while the estrone group had significantly lower, levels of cell survival (BrdU-ir cells) in the dentate gyrus compared to controls. Furthermore, rats injected with 17β-estradiol showed significantly higher levels of activation of new neurons in response to spatial memory compared to controls. These results provide insight into how estrogens differentially influence the brain and behavior, and may provide insight into the development of hormone replacement therapies for women.

Online redundant image elimination and its application to wireless capsule endoscopy

Digestive tract examination has now become painless and simple with the aid of wireless capsule endoscopy (WCE). By continuously imaging and transmitting the patient’s gastrointestinal tract, the capsule can store thousands of endoscopic images for medical diagnosis. The problem is that a large number of images generated in the near-time period are near-reduplicate and are therefore time-consuming for a medical expert to inspect. In this paper, we tackle this problem by proposing an online redundant image elimination system. Computer vision–based primitive features are first explored and compared to represent WCE images. A spatial sensitive version is then introduced to enhance the description. After determining the dissimilarity between neighboring images with a suitable measure, real-time and image-buffered versions of peak detection–based elimination algorithms are proposed to retain the distinctive/interesting images in the examination. Comparison results of primitive features and their spatial sensitive approaches via several probabilistic dissimilarity measures demonstrate that they are descriptive and efficient. Also, experiments performed on both the testing and the large real datasets show that the proposed elimination algorithms are effective, flexible and robust.

Brownian-time Brownian motion SIEs on $\mathbb{R}_{+}$ × $\mathbb{R}^d$: Ultra regular direct and lattice-limits solutions and fourth order SPDEs links

We delve deeper into the compelling regularizing effect of the Brownian-time Brownian motion density,$ \mathbb{K}^{{BTBM}^d}_{t;x,y}$ , on the space-time-white-noise-driven stochastic integral equation we call BTBM SIE:\begin{equation} U(t,x)=\int_{{\mathbb R}^{d}}{{\mathbb K}}^{\text{BTBM}^d}_{t;x,y} u_0(y) dy+ \int_{{\mathbb R}^{d}}\int_0^t{{\mathbb K}}^{\text{BTBM}^d}_{t-s;x,y} a(U(s,y))\mathscr W(ds\times dy), (0.1)\end{equation} which we recently introduced in [3].In sharp contrast to traditional second order heat-operator-based SPDEs---whose real-valued mild solutions are confined to $d=1$---we prove the existence of solutions to (0.1) in $d=1,2,3$ with dimension-dependent and striking Hölder regularity, under both less than Lipschitz and Lipschitz conditions on $a$. In space, we show an unprecedented nearly local Lipschitz regularity for $d=1,2$---roughly, $U$ is spatially twice as regular as the Brownian sheet in these dimensions---and we prove nearly local Hölder $1/2$ regularity in $d=3$. In time, our solutions are locally $\gamma$-Hölder continuous with exponent $γ∈(0, \frac{4-d}{8})$,$1≤d≤3$. To investigate (0.1) under less than Lipschitz conditions on $a$, we (a) introduce the Brownian-time random walk---a special case of lattice processes we call Brownian-time chains---and we use it to formulate the spatial lattice version of (0.1); and (b) develop a delicate variant of Stroock-Varadhan martingale approach, the K-martingale approach, tailor-made for a wide variety of kernel SIEs including (0.1) and the mild forms of many SPDEs of different orders on the lattice. Solutions to (0.1) are defined as limits of their lattice version.Along the way, we prove interesting aspects of Brownian-time random walk, including a fourth order differential-difference equation connection. We also prove existence, pathwise uniqueness, and the same Hölder regularity for (0.1), without discretization, in the Lipschitz case. The SIE (0.1) is intimately connected to intriguing fourth order SPDEs in two ways. First, we show that (0.1) is connected to the diagonals of a new unconventional fourth order SPDE we call parametrized BTBM SPDE. Second, replacing $ \mathbb {K}^{{BTBM}^d}_{t;x,y}$ , by the intimately connected kernel of our recently-introduced imaginary-Brownian-time-Brownian-angle process (IBTBAP), (0.1) becomes the mild form of a Kuramoto-Sivashinsky (KS) SPDE with linearized PDE part. Ideas and tools developed here are adapted in separate papers to give an entirely new approach, via our explicit IBTBAP representation, to many linear and nonlinear KS-type SPDEs in multi-spatial dimensions.

A New Proof of the Wiener-Hopf Factorization via Basu's Theorem

We illustrate how Basu's theorem can be used to derive the spatial version of the Wiener-Hopf factorization for a specific class of piecewise-deterministic Markov processes. The classical factorization results for both random walks and Lévy processes follow immediately from our result. The approach is particularly elegant when used to establish the factorization for spectrally one-sided Lévy processes.

A New Proof of the Wiener-Hopf Factorization via Basu's Theorem

We illustrate how Basu's theorem can be used to derive the spatial version of the Wiener-Hopf factorization for a specific class of piecewise-deterministic Markov processes. The classical factorization results for both random walks and Lévy processes follow immediately from our result. The approach is particularly elegant when used to establish the factorization for spectrally one-sided Lévy processes.

Stochastic Dynamics on Hypergraphs and the Spatial Majority Rule Model

This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of interactions with a structure of hypergraph. This new perspective is more appropriate to define stochastic spatial processes in which large blocks of vertices may flip simultaneously, which is then applied to define a spatial version of the Galam’s majority rule model. In our spatial model, each vertex of the lattice has one of two possible competing opinions, say opinion 0 and opinion 1, as in the popular voter model. Hyperedges are updated at rate one, which results in all the vertices in the hyperedge changing simultaneously their opinion to the majority opinion of the hyperedge. In the case of a tie in hyperedges with even size, a bias is introduced in favor of type 1, which is motivated by the principle of social inertia. Our analytical results along with simulations and heuristic arguments suggest that, in any spatial dimensions and when the set of hyperedges consists of the collection of all n×⋯×n blocks of the lattice, opinion 1 wins when n is even while the system clusters when n is odd, which contrasts with results about the voter model in high dimensions for which opinions coexist. This is fully proved in one dimension while the rest of our analysis focuses on the cases when n=2 and n=3 in two dimensions.

A spatial version of the Itô–Stratonovich correction

We consider a class of stochastic PDEs of Burgers type in spatial dimension 1, driven by space-time white noise. Even though it is well known that these equations are well posed, it turns out that if one performs a spatial discretization of the nonlinearity in the "wrong" way, then the sequence of approximate equations does converge to a limit, but this limit exhibits an additional correction term. This correction term is proportional to the local quadratic cross-variation (in space) of the gradient of the conserved quantity with the solution itself. This can be understood as a consequence of the fact that for any fixed time, the law of the solution is locally equivalent to Wiener measure, where space plays the role of time. In this sense, the correction term is similar to the usual It\^{o}-Stratonovich correction term that arises when one considers different temporal discretizations of stochastic ODEs.

Macroscopic mechanical correlations using single-photon spatial compass state and operational Wigner distribution

We propose a measurement scheme for observing quantum correlations and entanglement in the spatial properties of two macroscopic mirrors. Two spatial versions of compass states are generated by using a single Gaussian mode of single photons in a simple interferometer. The chessboard pattern of spatial compass states reflects the spatial properties of a mirror composed of $N$ quantum mirrors. The displacement and tilt correlations of the two mirrors are manifested by single photons and projection measurements through a measuring device which measures the propensities of the compass states. The technique can extract mechanical correlations of the two mirrors and lock them into the Einstein-Podolsky-Rosen (EPR) correlation. The criteria for EPR entanglement of these mirrors are then verified by sub-Planck structures in the propensity. We formulate the discrete-like property of the propensity, a demonstration of quantum jumps of EPR correlations in phase space, which, hence, enables discrete phase-space quantum computing and information processing.

Stochastic branching-diffusion models for gene expression.

A challenge to both understanding and modeling biochemical networks is integrating the effects of diffusion and stochasticity. Here, we use the theory of branching processes to give exact analytical expressions for the mean and variance of protein numbers as a function of time and position in a spatial version of an established model of gene expression. We show that both the mean and the magnitude of fluctuations are determined by the protein's Kuramoto length--the typical distance a protein diffuses over its lifetime--and find that the covariance between local concentrations of proteins often increases if there are substantial bursts of synthesis during translation. Using high-throughput data, we estimate that the Kuramoto length of cytoplasmic proteins in budding yeast to be an order of magnitude larger than the cell diameter, implying that many such proteins should have an approximately uniform concentration. For constitutively expressed proteins that live substantially longer than their mRNA, we give an exact expression for the deviation of their local fluctuations from Poisson fluctuations. If the Kuramoto length of mRNA is sufficiently small, we predict that such local fluctuations become approximately Poisson in bacteria in much of the cell, unless translational bursting is exceptionally strong. Our results therefore demonstrate that diffusion can act to both increase and decrease the complexity of fluctuations in biochemical networks.

Using Constrained Optimization for the Identification of Convergence Clubs

In the last years a central issue in regional economic growth debate is represented by the convergence problem. Many empirical economists have noticed that per-worker GDP of poor regions tend to converge to those of richer regions. However more recently it has been observed that the economic convergence might not be achieved if, in the empirical analysis, we consider the entire data set as one sample. The phenomenon should be analyzed considering regions as belonging to different sub-samples with quite similar economy. Many authors refer to this hypothesis as economic convergence clubs. The definition of these homogeneous groups represents a crucial issue in many regional economic growth studies. The aim of this paper is to propose a method for the identification of convergence clubs for the European regions at NUTS 2 level. The econometric specification used is based on the classical, and spatial augmented version of the conditional β-convergence model. Two different optimization algorithms for the identification of convergence clubs are proposed and compared: Simulated Annealing and Iterated Conditional Modes.

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This paper aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then, we consider Klimontovich's spatial stochastic version of the Boltzmann kinetic equation and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a subdomain of the continuum range, which the conventional Knudsen number classification does not account for appropriately. In this subdomain, it is possible to obtain a fully mechanically consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics.

Random mobility and the evolution of cooperation in spatial [formula omitted]-player iterated Prisoner’s Dilemma games

We study the effects of random mobility on the evolution of cooperation in a spatial version of the N-player Iterated Prisoner’s Dilemma game, where individuals are located on a two-dimensional regular lattice with periodic boundary conditions. The probability that an individual moves from its current location is based on the amount of time it has occupied a given position and the relative fitness values of the individual occupying the destination position. Our results show that random movement can promote cooperative behaviour in N-player games. In some circumstances, random mobility enhances system-wide cooperation levels when compared to the static model. However, the outcome is strictly dependent on the cost-to-benefit ratio and the range of movement. An analysis of the population dynamics suggests that the convergence rate of the model (i.e., the time for the population to reach an equilibrium state) is faster with mobility in place. Our findings help to further understand the relationship between mobility and evolving game-playing strategies in spatially structured populations, especially when efficient collective actions matter.

Dynamics of a Michaelis–Menten-type predation model incorporating a prey refuge withnoise and external forces

In this paper, we investigate a spatial version of a Michaelis–Menten-type predator–preymodel incorporating a prey refuge, which contains some important factors, such asenvironmental noise, external periodic forces and diffusion processes on both prey andpredator. Based on both mathematical analysis and numerical simulations, we get asufficient condition for diffusion instability with zero-flux boundary conditions. There is anincrease in the equilibrium density of both prey and predator as the prey refuge increasesunder a very restricted set of conditions. It is also proved that the refuge used by prey hasa stabilizing effect, that is, increases the local stability of the interior equilibrium.Moreover, due to the effects of environmental noise, we obtain the transition from regularpatterns to spatiotemporal chaotic dynamics in a corresponding spatially extended model.External periodic forces can induce 1:1 frequency-locking and spatially homogeneousoscillation to appear. Also the interaction between environmental noise and externalperiodic forces in the spatial model incorporating a prey refuge gives rise to a rich dynamicphenomenon.

Altered spatial learning and delay discounting in a rat model of human third trimester binge ethanol exposure

Ethanol exposure during perinatal development can cause cognitive abnormalities including difficulties in learning, attention, and memory, as well as heightened impulsivity. The purpose of this study was to assess performance in spatial learning and impulsive choice tasks in rats subjected to an intragastric intubation model of binge ethanol exposure during human third trimester-equivalent brain development. Male and female Sprague-Dawley rat pups were intubated with ethanol (5.25 g/kg/day) on postnatal days 4-9. At adolescence (between postnatal days 35-38), these rats and sham intubated within-litter controls were trained in both spatial and cued versions of the Morris water maze. A subset of the male rats was subsequently tested on a delay-discounting task to assess impulsive choice. Ethanol-exposed rats were spatially impaired relative to controls, but performed comparably to controls on the cued version of the water maze. Ethanol-exposed rats also showed greater preference for large delayed rewards on the delay discounting task, but no evidence for altered reward sensitivity or perseverative behavior. These data demonstrate that early postnatal intermittent binge-like ethanol exposure has prolonged, detrimental, but selective effects on cognition, suggesting that even relatively brief ethanol exposure late in human pregnancy can be deleterious for cognitive function.

Microinjection of Dihydrotestosterone as a 5α-Reduced Metabolite of Testosterone into CA1 Region of Hippocampus Could Improve Spatial Learning in the Adult Male Rats.

CA1 region of hippocampus has an important role in learning and memory. Previous reports have shown that androgens like testosterone and its metabolites are present in high concentration in CA1 region of hippocampus. Androgen receptors have also high density in this region. Therefore, it is suggested that neurohormones in CA1 have an important role in learning and memory. It is likely that testosterone exerts its effect via its metabolites, especially dihydrotestosterone (DHT), a 5α-reduced androgen. In this research, we conducted an experiment to assess the path of testosterone›s effectiveness on spatial learning and memory. Adult male rats were randomly divided into 4 groups and, bilaterally, cannulated into CA1 region of hippocampus. One week after the surgery, animals received DMSO 0.5 μL as a control group and different doses of dihydrotestosterone (DHT) (0.25, 0.5 and 1 µg/0.5 μL/side) 25-30 min before the training in spatial version of Morris Water Maze task. Training session contained two blocks which animals had to learn the position of hidden platform in 4 trials. On the test session (next day), rats performed a one-trial probe test and then a visible platform one. The results showed that escape latency and traveled distance were decreased significantly in DHT-treated (0.5 µg/0.5 μL/side) rats. This finding suggested that DHT may have improved the effect on acquisition of spatial learning and memory.

An Uninterpreted Spatial Version of the Trust Game: Evidence of Reciprocity Without Suggestive Words, Evidence of Iterated Dominance Self-Taught

In this working paper we report on two trust games: a BDM-like game which is interpreted through its use of the possibly suggestive words “show up fee,” “sends,” “tripled,” “send back”; and an uninterpreted spatial game that does not use these words suggestive or not. In the spatial game we found a considerable amount of reciprocity, which implies the words are not necessary for reciprocity. For further comparison we designed the two games to have a correspondence relation (the relation extends to the original BDM trust game). We focused on two “variables” – interpreted or uninterpreted and spatial or word-based. We also designed “constants” which were identical or near identical in the two games. We did this to reduce confounding in statistical comparisons. We found the frequency of reciprocity in the spatial game, without the suggestive words, was about the same as the frequency of reciprocity in the BDM-like game, with the suggestive words. We found iterated dominance in the spatial game was 5.5 times higher than in the BDM-like game. And we found sending the full endowment was significantly more frequent in the BDM-like game than in the spatial game.

Impacts of extreme weather on wheat and maize in France: evaluating regional crop simulations against observed data

Extreme weather conditions can strongly affect agricultural production, with negative impacts that can at times be detected at regional scales. In France, crop yields were greatly influenced by drought and heat stress in 2003 and by extremely wet conditions in 2007. Reported regional maize and wheat yields where historically low in 2003; in 2007 wheat yields were lower and maize yields higher than long-term averages. An analysis with a spatial version (10 × 10 km) of the EPIC crop model was tested with regards to regional crop yield anomalies of wheat and maize resulting from extreme weather events in France in 2003 and 2007, by comparing simulated results against reported regional crops statistics, as well as using remotely sensed soil moisture data. Causal relations between soil moisture and crop yields were specifically analyzed. Remotely sensed (AMSR-E) JJA soil moisture correlated significantly with reported regional crop yield for 2002–2007. The spatial correlation between JJA soil moisture and wheat yield anomalies was positive in dry 2003 and negative in wet 2007. Biweekly soil moisture data correlated positively with wheat yield anomalies from the first half of June until the second half of July in 2003. In 2007, the relation was negative the first half of June until the second half of August. EPIC reproduced observed soil dynamics well, and it reproduced the negative wheat and maize yield anomalies of the 2003 heat wave and drought, as well as the positive maize yield anomalies in wet 2007. However, it did not reproduce the negative wheat yield anomalies due to excessive rains and wetness in 2007. Results indicated that EPIC, in line with other crop models widely used at regional level in climate change studies, is capable of capturing the negative impacts of droughts on crop yields, while it fails to reproduce negative impacts of heavy rain and excessively wet conditions on wheat yield, due to poor representations of critical factors affecting plant growth and management. Given that extreme weather events are expected to increase in frequency and perhaps severity in coming decades, improved model representation of crop damage due to extreme events is warranted in order to better quantify future climate change impacts and inform appropriate adaptation responses.

Taylor's Law holds in experimental bacterial populations but competition does not influence the slope

Populations vary in time and in space, and temporal variation may differ from spatial variation. Yet, in the past half century, field data have confirmed both the temporal and spatial forms of Taylor's power Law, a linear relationship between log(variance) and log(mean) of population size. Recent theory predicted that competitive species interactions should reduce the slope of the temporal version of Taylor's Law. We tested whether this prediction applied to the spatial version of Taylor's Law using simple, well-controlled laboratory populations of two species of bacteria that were cultured either separately or together for 24 h in media of widely varying nutrient richness. Experimentally, the spatial form of Taylor's Law with a slope of 2 held for these simple bacterial communities, but competitive interactions between the two species did not reduce the spatial Taylor's Law slope. These results contribute to the widespread usefulness of Taylor's Law in population ecology, epidemiology and pest control.

Ghrelin-Attenuated Cognitive Dysfunction in Streptozotocin-induced Diabetic Rats

Diabetic encephalopathy is clinically characterized by acquired behavior and cognitive dysfunction but its pathogenesis is not clear. This study aimed to explore the pathogenesis of diabetic encephalopathy and the mechanisms of ghrelin to ameliorate cognitive dysfunction in diabetic rats. Thirty-six streptozotocin diabetic rat models were established; 12 weeks later, all the rats were randomly divided into 3 groups [diabetic model group (D), ghrelin treatment group (T1), and ghrelin and D-lys-3-GHRP-6 treatment group (T2)] of 12 each. Twelve normoglycemic rats were classified in the normal group (N). Learning and memory behaviors were measured using a spatial version of the Morris water maze test. The brain-derived neurotrophic factor (BDNF), cAMP responsive element binding protein (CREB), phosphorylated CREB (p-CREB), phosphorylated ERK1/2 (p-ERK1/2), caspase-3, and Bcl-xl protein expressions in the hippocampi of all the rats were detected using immunohistochemistry. The mRNA expressions of BDNF, CREB, and caspase-3 were examined using reverse transcription-polymerase chain reaction. The hippocampus neuronal apoptosis was measured by terminal deoxynucleotidyl transferase dUTP nick end labeling method. We found that learning and memory level in the ghrelin treatment group improved significantly, expression of Bcl-xl, BDNF, CREB, p-CREB, and p-ERK1/2 in the hippocampus was increased in the ghrelin treatment group, and the number of apoptotic neurons in the hippocampus decreased remarkably. Our results showed that the changes of BDNF, CREB, and hippocampus neuronal apoptosis might be involved in the pathogenesis of diabetic encephalopathy. We suggested that ghrelin improved cognitive ability in streptozotocin-induced diabetic rats by improving the expressions of BDNF and CREB and by attenuating hippocampus neuronal apoptosis. The effects of ghrelin depend on the receptor of ghrelin, GHSR-1a, and ERK1/2 pathway.

Early effects of emotion on word immediate repetition priming: Electrophysiological and source localization evidence

The processing of a stimulus benefits from the previous exposure of an identical stimulus, which is known as immediate repetition priming (IRP). Although several experimental manipulations modulate the size of this effect, the influence of affective information is still unclear. In order to explore the temporo-spatial characteristics of the interaction between emotion and IRP, event-related potentials (ERPs) to negative and neutral target words were measured during a lexical decision task in an IRP paradigm. Temporal and spatial versions of principal components analyses were used to detect and quantify those ERP components associated with IRP. A source localization procedure provided information on the neural origin of these components. Behavioural analyses showed that reaction times to repeated negative and neutral words differed from those to unrepeated negative and neutral words, respectively. However, the interaction between repetition and emotion was only marginally significant. In contrast, ERP analyses revealed specific IRP effects for negative words: Repeated negative words elicited reduced P120/enhanced N170 effects and weaker activation suppression in the left inferior frontal gyrus than did unrepeated negative words. These results suggest that a word's negative content captures attention interfering with IRP mechanisms, possibly at an early semantic stage of processing.