Nonlinear Attitude Filtering: A Comparison Study

This paper contains a concise comparison of a number of nonlinear attitude filtering methods that have attracted attention in the robotics and aviation literature. With the help of previously published surveys and comparison studies, the vast literature on the subject is narrowed down to a small pool of competitive attitude filters. Amongst these filters is a second-order optimal minimum-energy filter recently proposed by the authors. Easily comparable discretized unit quaternion implementations of the selected filters are provided. We conduct a simulation study and compare the transient behaviour and asymptotic convergence of these filters in two scenarios with different initialization and measurement errors inspired by applications in unmanned aerial robotics and space flight. The second-order optimal minimum-energy filter is shown to have the best performance of all filters, including the industry standard multiplicative extended Kalman filter (MEKF)

Fuzzy coprimary submodules

Let $R$ be a commutative ring with non-zero identity and let $M$ be a non-zero unitary $R$-module. The concept of fuzzy coprimary submodule as a dual notion of fuzzy primary one will be introduced and some of its properties will be studied. Among other things, the behavior of this concept with respect to fuzzy localization formation and fuzzy quotient will be examined

Revolutionaries and spies: Spy-good and spy-bad graphs

We study a game on a graph $G$ played by $r$ {\it revolutionaries} and $s$ {\it spies}. Initially, revolutionaries and then spies occupy vertices. In each subsequent round, each revolutionary may move to a neighboring vertex or not move, and then each spy has the same option. The revolutionaries win if $m$ of them meet at some vertex having no spy (at the end of a round); the spies win if they can avoid this forever. Let $\sigma(G,m,r)$ denote the minimum number of spies needed to win. To avoid degenerate cases, assume |V(G)|\ge r-m+1\ge\floor{r/m}\ge 1. The easy bounds are then \floor{r/m}\le \sigma(G,m,r)\le r-m+1. We prove that the lower bound is sharp when $G$ has a rooted spanning tree $T$ such that every edge of $G$ not in $T$ joins two vertices having the same parent in $T$. As a consequence, \sigma(G,m,r)\le\gamma(G)\floor{r/m}, where $\gamma(G)$ is the domination number; this bound is nearly sharp when $\gamma(G)\le m$. For the random graph with constant edge-probability $p$, we obtain constants $c$ and $c'$ (depending on $m$ and $p$) such that $\sigma(G,m,r)$ is near the trivial upper bound when $r<c\ln n$ and at most $c'$ times the trivial lower bound when $r>c'\ln n$. For the hypercube $Q_d$ with $d\ge r$, we have $\sigma(G,m,r)=r-m+1$ when $m=2$, and for $m\ge 3$ at least $r-39m$ spies are needed. For complete $k$-partite graphs with partite sets of size at least $2r$, the leading term in $\sigma(G,m,r)$ is approximately $\frac{k}{k-1}\frac{r}{m}$ when $k\ge m$. For $k=2$, we have \sigma(G,2,r)=\bigl\lceil{\frac{\floor{7r/2}-3}5}\bigr\rceil and \sigma(G,3,r)=\floor{r/2}, and in general $\frac{3r}{2m}-3\le \sigma(G,m,r)\le\frac{(1+1/\sqrt3)r}{m}$.Comment: 34 pages, 2 figures. The most important changes in this revision are improvements of the results on hypercubes and random graphs. The proof of the previous hypercube result has been deleted, but the statement remains because it is stronger for m<52. In the random graph section we added a spy-strategy resul

Temperature Shifts for Extraction and Purification of Zygomycetes Chitosan with Dilute Sulfuric Acid

The temperature-dependent hydrolysis and solubility of chitosan in sulfuric acid solutions offer the possibility for chitosan extraction from zygomycetes mycelia and separation from other cellular ingredients with high purity and high recovery. In this study, Rhizomucor pusillus biomass was initially extracted with 0.5 M NaOH at 120 °C for 20 min, leaving an alkali insoluble material (AIM) rich in chitosan. Then, the AIM was subjected to two steps treatment with 72 mM sulfuric acid at (i) room temperature for 10 min followed by (ii) 120 °C for 45 min. During the first step, phosphate of the AIM was released into the acid solution and separated from the chitosan-rich residue by centrifugation. In the second step, the residual AIM was re-suspended in fresh 72 mM sulfuric acid, heated at 120 °C and hot filtered, whereby chitosan was extracted and separated from the hot alkali and acid insoluble material (HAAIM). The chitosan was recovered from the acid solution by precipitation at lowered temperature and raised pH to 8–10. The treatment resulted in 0.34 g chitosan and 0.16 g HAAIM from each gram AIM. At the start, the AIM contained at least 17% phosphate, whereas after the purification, the corresponding phosphate content of the obtained chitosan was just 1%. The purity of this chitosan was higher than 83%. The AIM subjected directly to the treatment with hot sulfuric acid (at 120 °C for 45 min) resulted in a chitosan with a phosphate impurity of 18.5%

Identifying Retweetable Tweets with a Personalized Global Classifier

In this paper we present a method to identify tweets that a user may find interesting enough to retweet. The method is based on a global, but personalized classifier, which is trained on data from several users, represented in terms of user-specific features. Thus, the method is trained on a sufficient volume of data, while also being able to make personalized decisions, i.e., the same post received by two different users may lead to different classification decisions. Experimenting with a collection of approx.\ 130K tweets received by 122 journalists, we train a logistic regression classifier, using a wide variety of features: the content of each tweet, its novelty, its text similarity to tweets previously posted or retweeted by the recipient or sender of the tweet, the network influence of the author and sender, and their past interactions. Our system obtains F1 approx. 0.9 using only 10 features and 5K training instances.Comment: This is a long paper version of the extended abstract titled "A Personalized Global Filter To Predict Retweets", of the same authors, which was published in the 25th ACM UMAP conference in Bratislava, Slovakia, in July 201

Estimating the mechanical anisotropy of the Iranian lithosphere using the wavelet coherence method

We calculated anisotropic wavelet coherence between Bouguer anomaly and topography in order to map the anisotropy of the effective elastic thickness of the Iranian lithosphere (Te). An orthotropic elastic plate model is used for inverting the anisotropic wavelet coherence to compute the mechanical anisotropy through the weak axis of the Te. Anisotropy of the Te-weak axis and the strength of the anisotropic parameter, namely the anisotropic coherence effect over the study area are estimated by restricting the rotated Morlet wavelet (fan wavelet) geometry over an azimuthal range of 90°. Large-scale Te variations have been shown to be associated with phenomena, such as mountain belts, subduction zones, craton boundaries, fault zones, and seismogenic regions. Although the correlation between the major tectonic features of the Iranian lithosphere and the distribution of the Te-weak axis is not general or precise, in some regions, such as the Central Iran Blocks, and the Alborz, Kopeh Dagh, Zagros, and Makran orogenic belts, the weak axis has a uniform or slowly varying pattern which changes over their boundaries. A perpendicular alignment between seismic anisotropy measurements in Iran and the Te-weak directions suggests a lithospheric origin for anisotropy. The correlation between averaged stress directions and the weak axis of the Te in Iran indicates that the present day stress field and the fossil strain are still related. Correlation between these factors suggests vertically coherent deformation of the lithosphere in Iran resulting from the multiply convergent orogenic processes. The complex mechanical anisotropy pattern of the Iranian lithosphere results from the interaction of many pre-existent structures which dominantly control the mechanical anisotropy of the lithosphere

Relevance-based Word Embedding

Learning a high-dimensional dense representation for vocabulary terms, also known as a word embedding, has recently attracted much attention in natural language processing and information retrieval tasks. The embedding vectors are typically learned based on term proximity in a large corpus. This means that the objective in well-known word embedding algorithms, e.g., word2vec, is to accurately predict adjacent word(s) for a given word or context. However, this objective is not necessarily equivalent to the goal of many information retrieval (IR) tasks. The primary objective in various IR tasks is to capture relevance instead of term proximity, syntactic, or even semantic similarity. This is the motivation for developing unsupervised relevance-based word embedding models that learn word representations based on query-document relevance information. In this paper, we propose two learning models with different objective functions; one learns a relevance distribution over the vocabulary set for each query, and the other classifies each term as belonging to the relevant or non-relevant class for each query. To train our models, we used over six million unique queries and the top ranked documents retrieved in response to each query, which are assumed to be relevant to the query. We extrinsically evaluate our learned word representation models using two IR tasks: query expansion and query classification. Both query expansion experiments on four TREC collections and query classification experiments on the KDD Cup 2005 dataset suggest that the relevance-based word embedding models significantly outperform state-of-the-art proximity-based embedding models, such as word2vec and GloVe.Comment: to appear in the proceedings of The 40th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR '17

New Privacy Mechanism Design With Direct Access to the Private Data

The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A statistical privacy mechanism is employed to generate data $U$ based on $(X,Y)$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. To this end, we use extended versions of the Functional Representation Lemma and Strong Functional Representation Lemma and combine them with a simple observation which we call separation technique. New lower bounds on privacy-utility trade-off are derived and we show that they can improve the previous bounds. We study the obtained bounds in different scenarios and compare them with previous results.Comment: arXiv admin note: substantial text overlap with arXiv:2201.08738, arXiv:2212.1247