The behavior of the NPMLE of a decreasing density near the boundaries of the support

We investigate the behavior of the nonparametric maximum likelihood estimator $\hat{f}_n$ for a decreasing density $f$ near the boundaries of the support of $f$. We establish the limiting distribution of $\hat{f}_n(n^{-\alpha})$, where we need to distinguish between different values of $0<\alpha<1$. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of $f$ at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.Comment: Published at http://dx.doi.org/10.1214/009053606000000100 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic normality of the LkL_k-error of the Grenander estimator

We investigate the limit behavior of the $L_k$-distance between a decreasing density $f$ and its nonparametric maximum likelihood estimator $\hat{f}_n$ for $k\geq1$. Due to the inconsistency of $\hat{f}_n$ at zero, the case $k=2.5$ turns out to be a kind of transition point. We extend asymptotic normality of the $L_1$-distance to the $L_k$-distance for $1\leq k<2.5$, and obtain the analogous limiting result for a modification of the $L_k$-distance for $k\geq2.5$. Since the $L_1$-distance is the area between $f$ and $\hat{f}_n$, which is also the area between the inverse $g$ of $f$ and the more tractable inverse $U_n$ of $\hat{f}_n$, the problem can be reduced immediately to deriving asymptotic normality of the $L_1$-distance between $U_n$ and $g$. Although we lose this easy correspondence for $k>1$, we show that the $L_k$-distance between $f$ and $\hat{f}_n$ is asymptotically equivalent to the $L_k$-distance between $U_n$ and $g$.Comment: Published at http://dx.doi.org/10.1214/009053605000000462 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates

We study the following computational problem: for which values of k, the majority of n bits MAJ_n can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJ_k o MAJ_k. We observe that the minimum value of k for which there exists a MAJ_k o MAJ_k circuit that has high correlation with the majority of n bits is equal to Theta(sqrt(n)). We then show that for a randomized MAJ_k o MAJ_k circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n^(2/3+o(1)). We show a worst case lower bound: if a MAJ_k o MAJ_k circuit computes the majority of n bits correctly on all inputs, then k <= n^(13/19+o(1)). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k= O(n^(2/3)) can compute MAJ_n correctly on all inputs

Voice and Emphasis in Arabic Coronal Stops: Evidence for Phonological Compensation

The current study investigates multiple acoustic cues–voice onset time (VOT), spectral center of gravity (SCG) of burst, pitch (F0), and frequencies of the first (F1) and second (F2) formants at vowel onset—associated with phonological contrasts of voicing and emphasis in production of Arabic coronal stops. The analysis of the acoustic data collected from eight native speakers of the Qatari dialect showed that the three stops form three distinct modes on the VOT scale: [d] is (pre)voiced, voiceless [t] is aspirated, and emphatic [ṭ] is voiceless unaspirated. The contrast is also maintained in spectral cues. Each cue influences production of coronal stops while their relevance to phonological contrasts varies. VOT was most relevant for voicing, but F2 was mostly associated with emphasis. The perception experiment revealed that listeners were able to categorize ambiguous tokens correctly and compensate for phonological contrasts. The listeners’ results were used to evaluate three categorization models to predict the intended category of a coronal stop: a model with unweighted and unadjusted cues, a model with weighted cues compensating for phonetic context, and a model with weighted cues compensating for the voicing and emphasis contrasts. The findings suggest that the model with phonological compensation performed most similar to human listeners both in terms of accuracy rate and error pattern

Effect of emphasis spread on coronal stop articulation in Qatari Arabic

Emphasis (contrastive uvularisation) in Arabic spreads from an emphatic consonant to neighboring segments (Davis1995). The effect of emphasis spread on a consonant is manifested as lowering of its spectral mean (Jongman et al.2011). Although stop consonants reveal a strong effect of emphasis, it is not known how emphasis spread affects other acoustic properties of stops, e.g. voice onset time (VOT). Previous studies(Kulikov2018)showed that VOT and emphasis are linked in speech production: plain /t/in Gulf Arabic is aspirated; emphatic /ṭ/has short-lag VOT. Phonological theory predicts that plain /t/should become more emphatic in emphatic context, which might reduce stopVOTas well.The current study investigates the effect of emphasisspread on VOT in word-initial coronal stops in Qatari Arabic. The stimuli, produced bysixteen native speakers of Qatari Arabic,contained target plain and emphatic stops /t/, /ṭ/followed by short or long low vowel, and plain coronal obstruents /t, s, ð/or their emphatic counterparts /ṭ, ṣ, ð/. The acoustic analysis included measurements of VOT and spectral mean of burst in the stop, and F1, F2, F3 frequencies at the vowel beginning, middle and end. The results showed that final emphatic obstruent triggered emphasis spread across the syllable. The effect of emphasis on the vowel was stronger next to the emphatic obstruent (p < .01). Spectral mean of burst in plain /t/was lower in the emphatic context (D = 276 Hz, p = .05). VOT, however, was not affected by emphasis spread. Plain /t/had long-lag VOT averaging 52 ms; emphatic /ṭ/had short-lag VOT averaging 17 ms. These values were not different in emphatic context (p = .743).The findings demonstrate that emphasis spread within a syllableaffects only spectral characteristics of a coronal stop. Emphaticness of plain /t/did not affect its VOT and did not result in complete transformation of the stop category

Discrete and analog evaluation of the capillary-pore space of foam concrete in eco-friendly production

Relevance. The aim of the study was to identify and study the analytical dependencies of technological parameters and aspects of the preparation of foam concrete depending on the concentration of foaming agents at various points in the formation of the capillary-porous structure. It is important to evaluate the possibility of using them to obtain environmentally friendly performance properties of “poro-concrete”, as it is often used in the construction of agricultural facilities. In the course of optical studies, the carbon footprint in the components of the composite materials under study was tracked. The distribution of pore sizes across auto-modal clusters is determined. Dispersion analysis of surface sections of foam concrete was carried out. Based on the discrete analysis of the concrete structure, analog analytical dependences were obtained linking the studied properties of foam concrete with the parameters of density, eco-friendly, porosity, and other parameters. In the construction of agricultural facilities these properties are particularly important

An Edit Friendly DDPM Noise Space: Inversion and Manipulations

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g., shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity

The limit distribution of the L∞L_{\infty}-error of Grenander-type estimators

Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of $[0,1]$. The rate of convergence is found to be of order $(n/\log n)^{-1/3}$ and the limiting distribution to be Gumbel.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1015 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org