Massey products in symplectic manifolds

The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are exposed. The construction uses the symplectic blow-up and is based on the author results, which describe conditions under which the blow-up of a symplectic manifold X along its submanifold Y inherits nontrivial Massey products from X ot Y. This gives a general construction of nonformal symplectic manifolds.Comment: LaTeX, 48 pages, 2 figure

Special Moduli of Continuity and the Constant in the Jackson-Stechkin Theorem

We consider a special 2k-order modulus of continuity W 2k(f,h) of 2π-periodic continuous functions and prove an analog of the Bernstein-Nikolsky-Stechkin inequality for trigonometric polynomials in terms of W 2k. We simplify the main construction from the paper by Foucart et al. (Constr. Approx. 29(2), 157-179, 2009) and give new upper estimates of the Jackson-Stechkin constants. The inequality W2k(f,h)≤3∥f∥∞ and the Bernstein-Nikolsky-Stechkin type estimate imply the Jackson-Stechkin theorem with nearly optimal constant for approximation by periodic splines. © 2013 The Author(s)

Wavelet Trees Meet Suffix Trees

We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings. Given a string of length n over an alphabet of size $\sigma\leq n$, our method builds the wavelet tree in $O(n \log \sigma/ \sqrt{\log{n}})$ time, improving upon the state-of-the-art algorithm by a factor of $\sqrt{\log n}$. As a consequence, given an array of n integers we can construct in $O(n \sqrt{\log n})$ time a data structure consisting of $O(n)$ machine words and capable of answering rank/select queries for the subranges of the array in $O(\log n / \log \log n)$ time. This is a $\log \log n$-factor improvement in query time compared to Chan and P\u{a}tra\c{s}cu and a $\sqrt{\log n}$-factor improvement in construction time compared to Brodal et al. Next, we switch to stringological context and propose a novel notion of wavelet suffix trees. For a string w of length n, this data structure occupies $O(n)$ words, takes $O(n \sqrt{\log n})$ time to construct, and simultaneously captures the combinatorial structure of substrings of w while enabling efficient top-down traversal and binary search. In particular, with a wavelet suffix tree we are able to answer in $O(\log |x|)$ time the following two natural analogues of rank/select queries for suffixes of substrings: for substrings x and y of w count the number of suffixes of x that are lexicographically smaller than y, and for a substring x of w and an integer k, find the k-th lexicographically smallest suffix of x. We further show that wavelet suffix trees allow to compute a run-length-encoded Burrows-Wheeler transform of a substring x of w in $O(s \log |x|)$ time, where s denotes the length of the resulting run-length encoding. This answers a question by Cormode and Muthukrishnan, who considered an analogous problem for Lempel-Ziv compression

PlaNet - Photo Geolocation with Convolutional Neural Networks

Is it possible to build a system to determine the location where a photo was taken using just its pixels? In general, the problem seems exceptionally difficult: it is trivial to construct situations where no location can be inferred. Yet images often contain informative cues such as landmarks, weather patterns, vegetation, road markings, and architectural details, which in combination may allow one to determine an approximate location and occasionally an exact location. Websites such as GeoGuessr and View from your Window suggest that humans are relatively good at integrating these cues to geolocate images, especially en-masse. In computer vision, the photo geolocation problem is usually approached using image retrieval methods. In contrast, we pose the problem as one of classification by subdividing the surface of the earth into thousands of multi-scale geographic cells, and train a deep network using millions of geotagged images. While previous approaches only recognize landmarks or perform approximate matching using global image descriptors, our model is able to use and integrate multiple visible cues. We show that the resulting model, called PlaNet, outperforms previous approaches and even attains superhuman levels of accuracy in some cases. Moreover, we extend our model to photo albums by combining it with a long short-term memory (LSTM) architecture. By learning to exploit temporal coherence to geolocate uncertain photos, we demonstrate that this model achieves a 50% performance improvement over the single-image model

PinnerSage: Multi-Modal User Embedding Framework for Recommendations at Pinterest

Latent user representations are widely adopted in the tech industry for powering personalized recommender systems. Most prior work infers a single high dimensional embedding to represent a user, which is a good starting point but falls short in delivering a full understanding of the user's interests. In this work, we introduce PinnerSage, an end-to-end recommender system that represents each user via multi-modal embeddings and leverages this rich representation of users to provides high quality personalized recommendations. PinnerSage achieves this by clustering users' actions into conceptually coherent clusters with the help of a hierarchical clustering method (Ward) and summarizes the clusters via representative pins (Medoids) for efficiency and interpretability. PinnerSage is deployed in production at Pinterest and we outline the several design decisions that makes it run seamlessly at a very large scale. We conduct several offline and online A/B experiments to show that our method significantly outperforms single embedding methods.Comment: 10 pages, 7 figure

On the linear independence of spikes and sines

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof involves depends on an extrapolation argument of Bourgain and Tzafriri.Comment: 16 pages, 4 figures. Revision with new proof of major theorem

Fixed nitrogen in agriculture and its role in agrocenoses

Received: February 23rd, 2021 ; Accepted: May 12th, 2021 ; Published: May 19th, 2021 ; Correspondence: [email protected] typical low-humus black soils in short crop rotations with legumes (25–33%) and without them, it was found that depending on the set of crops in crop rotation and application of fertilizer rates, nitrogen yield per crop is from 355 kg ha-1 to 682 kg ha-1 . The recommended fertilization system provided nitrogen compensation for crop yields by only 31–76%. Hence, in the plant-fertilizer system nitrogen deficiency varies from 161 to 370 kg ha-1 . The greatest nitrogen deficiency in the soil is observed in crop rotation without the use of fertilizers with the following crop rotation: peas-winter wheat-grain maize-spring barley. The main source of nitrogen for plants is soil nitrogen. In crop rotations with legumes, biological nitrogen is supplied from the air, which in quantitative terms per rotation in crop rotations with peas is 109–288 kg ha-1 , with soybeans 264–312, and with alfalfa 486 kg ha-1 . Biological nitrogen in crop rotations with peas and soybeans is reimbursed from 25 to 62%, in crop rotation without legumes - 9% (non-symbiotic nitrogen fixation), and in crop rotation with alfalfa - 89% of the total nitrogen removal with the crop

Pluronic F127 thermosensitive injectable smart hydrogels for controlled drug delivery system development

YesUnderstanding structure-property relationships is critical for the development of new drug delivery systems. This study investigates the properties of Pluronic smart hydrogel formulations for future use as injectable controlled drug carriers. The smart hydrogels promise to enhance patient compliance, decrease side effects and reduce dose and frequency. Pharmaceutically, these systems are attractive due to their unique sol-gel phase transition in the body, biocompatibility, safety and injectability as solutions before transforming into gel matrices at body temperature. We quantify the structural changes of F127 systems under controlled temperature after flow, as experienced during real bodily injection. Empirical formulae combining the coupled thermal and shear dependency are produced to aid future application of these systems. Induced structural transitions measured in-situ by small angle x-ray and neutron scattering reveal mixed oriented structures that can be exploited to tailor the drug release profile

Learning Rotation Adaptive Correlation Filters in Robust Visual Object Tracking

Visual object tracking is one of the major challenges in the field of computer vision. Correlation Filter (CF) trackers are one of the most widely used categories in tracking. Though numerous tracking algorithms based on CFs are available today, most of them fail to efficiently detect the object in an unconstrained environment with dynamically changing object appearance. In order to tackle such challenges, the existing strategies often rely on a particular set of algorithms. Here, we propose a robust framework that offers the provision to incorporate illumination and rotation invariance in the standard Discriminative Correlation Filter (DCF) formulation. We also supervise the detection stage of DCF trackers by eliminating false positives in the convolution response map. Further, we demonstrate the impact of displacement consistency on CF trackers. The generality and efficiency of the proposed framework is illustrated by integrating our contributions into two state-of-the-art CF trackers: SRDCF and ECO. As per the comprehensive experiments on the VOT2016 dataset, our top trackers show substantial improvement of 14.7% and 6.41% in robustness, 11.4% and 1.71% in Average Expected Overlap (AEO) over the baseline SRDCF and ECO, respectively.Comment: Published in ACCV 201