Benjamin Eltzner, Stephan F. Huckemann.

Source: The Annals of Statistics, Volume 47, Number 6, 3360--3381.

Abstract:
The (CLT) central limit theorems for generalized Fréchet means (data descriptors assuming values in manifolds, such as intrinsic means, geodesics, etc.) on manifolds from the literature are only valid if a certain empirical process of Hessians of the Fréchet function converges suitably, as in the proof of the prototypical BP-CLT [ Ann. Statist. 33 (2005) 1225–1259]. This is not valid in many realistic scenarios and we provide for a new very general CLT. In particular, this includes scenarios where, in a suitable chart, the sample mean fluctuates asymptotically at a scale $n^{alpha }$ with exponents $alpha <1/2$ with a nonnormal distribution. As the BP-CLT yields only fluctuations that are, rescaled with $n^{1/2}$, asymptotically normal, just as the classical CLT for random vectors, these lower rates, somewhat loosely called smeariness, had to date been observed only on the circle. We make the concept of smeariness on manifolds precise, give an example for two-smeariness on spheres of arbitrary dimension, and show that smeariness, although “almost never” occurring, may have serious statistical implications on a continuum of sample scenarios nearby. In fact, this effect increases with dimension, striking in particular in high dimension low sample size scenarios.

Benedikt Bauer, Michael Kohler.

Source: The Annals of Statistics, Volume 47, Number 4, 2261--2285.

Abstract:
Assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold, it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality in nonparametric regression. The proof is based on new approximation results concerning multilayer feedforward neural networks with bounded weights and a bounded number of hidden neurons. The estimates are compared with various other approaches by using simulated data.

Zhenguo Gao, Pang Du, Ran Jin, John L. Robertson.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 143--159.

Abstract:
Liver procurement experiments with surface-temperature monitoring motivated Gao et al. ( J. Amer. Statist. Assoc. 114 (2019) 773–781) to develop a variance change-point detection method under a smoothly-changing mean trend. However, the spotwise change points yielded from their method do not offer immediate information to surgeons since an organ is often transplanted as a whole or in part. We develop a new practical method that can analyze a defined portion of the organ surface at a time. It also provides a novel addition to the developing field of functional data monitoring. Furthermore, numerical challenge emerges for simultaneously modeling the variance functions of 2D locations and the mean function of location and time. The respective sample sizes in the scales of 10,000 and 1,000,000 for modeling these functions make standard spline estimation too costly to be useful. We introduce a multistage subsampling strategy with steps educated by quickly-computable preliminary statistical measures. Extensive simulations show that the new method can efficiently reduce the computational cost and provide reasonable parameter estimates. Application of the new method to our liver surface temperature monitoring data shows its effectiveness in providing accurate status change information for a selected portion of the organ in the experiment.

Carolyn M. Rutter, Jonathan Ozik, Maria DeYoreo, Nicholson Collier.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2189--2212.

Abstract:
Microsimulation models (MSMs) are used to inform policy by predicting population-level outcomes under different scenarios. MSMs simulate individual-level event histories that mark the disease process (such as the development of cancer) and the effect of policy actions (such as screening) on these events. MSMs often have many unknown parameters; calibration is the process of searching the parameter space to select parameters that result in accurate MSM prediction of a wide range of targets. We develop Incremental Mixture Approximate Bayesian Computation (IMABC) for MSM calibration which results in a simulated sample from the posterior distribution of model parameters given calibration targets. IMABC begins with a rejection-based ABC step, drawing a sample of points from the prior distribution of model parameters and accepting points that result in simulated targets that are near observed targets. Next, the sample is iteratively updated by drawing additional points from a mixture of multivariate normal distributions and accepting points that result in accurate predictions. Posterior estimates are obtained by weighting the final set of accepted points to account for the adaptive sampling scheme. We demonstrate IMABC by calibrating CRC-SPIN 2.0, an updated version of a MSM for colorectal cancer (CRC) that has been used to inform national CRC screening guidelines.

Javier Cárcamo, Antonio Cuevas, Luis-Alberto Rodríguez.

Source: Bernoulli, Volume 26, Number 3, 2143--2175.

Abstract:
We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and the amplitude of a function. The (usually non-linear) derivatives of these maps adopt simple expressions under suitable assumptions on the underlying space. As an application, we improve and extend to the multidimensional case the results in Raghavachari ( Ann. Statist. 1 (1973) 67–73) regarding the limiting distributions of Kolmogorov–Smirnov type statistics under the alternative hypothesis. Similar results are obtained for analogous statistics associated with copulas. We additionally solve an open problem about the Berk–Jones statistic proposed by Jager and Wellner (In A Festschrift for Herman Rubin (2004) 319–331 IMS). Finally, the asymptotic distribution of maximum mean discrepancies over Donsker classes of functions is derived.

Ulrike Mayer, Henryk Zähle, Zhou Zhou.

Source: Bernoulli, Volume 26, Number 3, 1891--1911.

Abstract:
We derive a functional weak limit theorem for a local empirical process of a wide class of piece-wise locally stationary (PLS) time series. The latter result is applied to derive the asymptotics of weighted empirical quantiles and weighted V-statistics of non-stationary time series. The class of admissible underlying time series is illustrated by means of PLS linear processes and PLS ARCH processes.

Kamran Kalbasi, Thomas Mountford.

Source: Bernoulli, Volume 26, Number 2, 1504--1534.

Abstract:
In this paper, we study the local times of vector-valued Gaussian fields that are ‘diagonally operator-self-similar’ and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the temporal unit hypercube by $Z$, we show that there exists $lambdain(0,1)$ such that under some quite weak conditions, $lim_{n ightarrow+infty}frac{sqrt[n]{mathbb{E}(Z^{n})}}{n^{lambda}}$ and $lim_{x ightarrow+infty}frac{-logmathbb{P}(Z>x)}{x^{frac{1}{lambda}}}$ both exist and are strictly positive (possibly $+infty$). Moreover, we show that if the underlying Gaussian field is ‘strongly locally nondeterministic’, the above limits will be finite as well. These results are then applied to establish similar statements for the intersection local times of diagonally operator-self-similar Gaussian fields with stationary increments.

Shuyang Bai, Murad S. Taqqu.

Source: Bernoulli, Volume 26, Number 2, 1473--1503.

Abstract:
We consider a long-memory stationary process, defined not through a moving average type structure, but by a flow generated by a measure-preserving transform and by a multiple Wiener–Itô integral. The flow is described using a notion of mixing for infinite-measure spaces introduced by Krickeberg (In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2 (1967) 431–446 Univ. California Press). Depending on the interplay between the spreading rate of the flow and the order of the multiple integral, one can recover known central or non-central limit theorems, and also obtain joint convergence of multiple integrals of different orders.

Wensheng Wang, Zhonggen Su, Yimin Xiao.

Source: Bernoulli, Volume 26, Number 2, 1410--1430.

Abstract:
We establish the exact moduli of non-differentiability of Gaussian random fields with stationary increments. As an application of the result, we prove that the uniform Hölder condition for the maximum local times of Gaussian random fields with stationary increments obtained in Xiao (1997) is optimal. These results are applicable to fractional Riesz–Bessel processes and stationary Gaussian random fields in the Matérn and Cauchy classes.

Emanuele Dolera, Stefano Favaro.

Source: Bernoulli, Volume 26, Number 2, 1294--1322.

Abstract:
Given a sequence ${X_{n}}_{ngeq 1}$ of exchangeable Bernoulli random variables, the celebrated de Finetti representation theorem states that $frac{1}{n}sum_{i=1}^{n}X_{i}stackrel{a.s.}{longrightarrow }Y$ for a suitable random variable $Y:Omega ightarrow [0,1]$ satisfying $mathsf{P}[X_{1}=x_{1},dots ,X_{n}=x_{n}|Y]=Y^{sum_{i=1}^{n}x_{i}}(1-Y)^{n-sum_{i=1}^{n}x_{i}}$. In this paper, we study the rate of convergence in law of $frac{1}{n}sum_{i=1}^{n}X_{i}$ to $Y$ under the Kolmogorov distance. After showing that a rate of the type of $1/n^{alpha }$ can be obtained for any index $alpha in (0,1]$, we find a sufficient condition on the distribution of $Y$ for the achievement of the optimal rate of convergence, that is $1/n$. Besides extending and strengthening recent results under the weaker Wasserstein distance, our main result weakens the regularity hypotheses on $Y$ in the context of the Hausdorff moment problem.

Klemm (Family)

ACT and the American Federation of Teachers are partnering to provide free resources as educators increasingly switch to distance learning amid the COVID-19 pandemic.

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Irune Diaz-Aparicio
Feb 12, 2020; 40:1453-1482
Development Plasticity Repair

Catherine Orr
Mar 6, 2019; 39:1817-1827
BehavioralSystemsCognitive

Welcoming remarks by Mr Fernando Restoy, Chairman, Financial Stability Institute, Bank for International Settlements, at the FSI-IADI conference on crisis management, resolution and deposit insurance: what's next and how to prepare, Basel, 4 September 2019.

On-the-record remarks of the March 2020 Quarterly Review media briefing by Mr Claudio Borio, Head of the Monetary and Economic Department, and Mr Hyun Song Shin, Economic Adviser and Head of Research, 28 February 2020.

Endogenous neuropeptide Y (NPY) and corticotrophin-releasing factor (CRF) modulate the responses of the basolateral amygdala (BLA) to stress and are associated with the development of stress resilience and vulnerability, respectively. We characterized persistent effects of repeated NPY and CRF treatment on the structure and function of BLA principal neurons in a novel organotypic slice culture (OTC) model of male rat BLA, and examined the contributions of specific NPY receptor subtypes to these neural and behavioral effects. In BLA principal neurons within the OTCs, repeated NPY treatment caused persistent attenuation of excitatory input and induced dendritic hypotrophy via Y₅ receptor activation; conversely, CRF increased excitatory input and induced hypertrophy of BLA principal neurons. Repeated treatment of OTCs with NPY followed by an identical treatment with CRF, or vice versa, inhibited or reversed all structural changes in OTCs. These structural responses to NPY or CRF required calcineurin or CaMKII, respectively. Finally, repeated intra-BLA injections of NPY or a Y₅ receptor agonist increased social interaction, a validated behavior for anxiety, and recapitulated structural changes in BLA neurons seen in OTCs, while a Y₅ receptor antagonist prevented NPY's effects both on behavior and on structure. These results implicate the Y₅ receptor in the long-term, anxiolytic-like effects of NPY in the BLA, consistent with an intrinsic role in stress buffering, and highlight a remarkable mechanism by which BLA neurons may adapt to different levels of stress. Moreover, BLA OTCs offer a robust model to study mechanisms associated with resilience and vulnerability to stress in BLA.

SIGNIFICANCE STATEMENT Within the basolateral amygdala (BLA), neuropeptide Y (NPY) is associated with buffering the neural stress response induced by corticotropin releasing factor, and promoting stress resilience. We used a novel organotypic slice culture model of BLA, complemented with in vivo studies, to examine the cellular mechanisms associated with the actions of NPY. In organotypic slice cultures, repeated NPY treatment reduces the complexity of the dendritic extent of anxiogenic BLA principal neurons, making them less excitable. NPY, via activation of Y5 receptors, additionally inhibits and reverses the increases in dendritic extent and excitability induced by the stress hormone, corticotropin releasing factor. This NPY-mediated neuroplasticity indicates that resilience or vulnerability to stress may thus involve neuropeptide-mediated dendritic remodeling in BLA principal neurons.

Functional recovery after cortical injury, such as stroke, is associated with neural circuit reorganization, but the underlying mechanisms and efficacy of therapeutic interventions promoting neural plasticity in primates are not well understood. Bone marrow mesenchymal stem cell-derived extracellular vesicles (MSC-EVs), which mediate cell-to-cell inflammatory and trophic signaling, are thought be viable therapeutic targets. We recently showed, in aged female rhesus monkeys, that systemic administration of MSC-EVs enhances recovery of function after injury of the primary motor cortex, likely through enhancing plasticity in perilesional motor and premotor cortices. Here, using in vitro whole-cell patch-clamp recording and intracellular filling in acute slices of ventral premotor cortex (vPMC) from rhesus monkeys (Macaca mulatta) of either sex, we demonstrate that MSC-EVs reduce injury-related physiological and morphologic changes in perilesional layer 3 pyramidal neurons. At 14-16 weeks after injury, vPMC neurons from both vehicle- and EV-treated lesioned monkeys exhibited significant hyperexcitability and predominance of inhibitory synaptic currents, compared with neurons from nonlesioned control brains. However, compared with vehicle-treated monkeys, neurons from EV-treated monkeys showed lower firing rates, greater spike frequency adaptation, and excitatory:inhibitory ratio. Further, EV treatment was associated with greater apical dendritic branching complexity, spine density, and inhibition, indicative of enhanced dendritic plasticity and filtering of signals integrated at the soma. Importantly, the degree of EV-mediated reduction of injury-related pathology in vPMC was significantly correlated with measures of behavioral recovery. These data show that EV treatment dampens injury-related hyperexcitability and restores excitatory:inhibitory balance in vPMC, thereby normalizing activity within cortical networks for motor function.

SIGNIFICANCE STATEMENT Neuronal plasticity can facilitate recovery of function after cortical injury, but the underlying mechanisms and efficacy of therapeutic interventions promoting this plasticity in primates are not well understood. Our recent work has shown that intravenous infusions of mesenchymal-derived extracellular vesicles (EVs) that are involved in cell-to-cell inflammatory and trophic signaling can enhance recovery of motor function after injury in monkey primary motor cortex. This study shows that this EV-mediated enhancement of recovery is associated with amelioration of injury-related hyperexcitability and restoration of excitatory-inhibitory balance in perilesional ventral premotor cortex. These findings demonstrate the efficacy of mesenchymal EVs as a therapeutic to reduce injury-related pathologic changes in the physiology and structure of premotor pyramidal neurons and support recovery of function.

The terraced hills of the Andes, the rice paddies of southern China, the oasis systems of the Maghreb: agriculture molds landscapes and places. Agriculture also shapes livelihoods, lifestyles, food traditions and cultures. What kind of plants grow or can’t grow, how they are harvested and what people eat define people’s lives.  Because our natural resources are under great strain, we need [...]

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