Search

Given a valued field $(K,v)$ and an irreducible polynomial $g\in K[x]$, we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaqui\'e and Herrera-Olalla-Mahboub-Spivakovsky, leading (under certain conditions) to an algorithm to find the factorization of $g$ over a henselization of $(K,v)$.

The Zwicky Transient Facility (ZTF) performs a systematic neutrino follow-up program, searching for optical counterparts to high-energy neutrinos with dedicated Target-of-Opportunity (ToO) observations. Since first light in March 2018, ZTF has taken prompt observations for 24 high-quality neutrino alerts from the IceCube Neutrino Observatory, with a median latency of 12.2 hours from initial neutrino detection. From two of these campaigns, we have already reported tidal disruption event (TDE) AT 2019dsg and likely TDE AT 2019fdr as probable counterparts, suggesting that TDEs contribute >7.8% of the astrophysical neutrino flux. We here present the full results of our program through to December 2021. No additional candidate neutrino sources were identified by our program, allowing us to place the first constraints on the underlying optical luminosity function of astrophysical neutrino sources. Transients with optical absolutes magnitudes brighter that $-21$ can contribute no more than 87% of the total, while transients brighter than $-22$ can contribute no more than 58% of the total, neglecting the effect of extinction and assuming they follow the star formation rate. These are the first observational constraints on the neutrino emission of bright populations such as superluminous supernovae. None of the neutrinos were coincident with bright optical AGN flares comparable to that observed for TXS 0506+056/IC170922A, with such optical blazar flares producing no more than 26% of the total neutrino flux. We highlight the outlook for electromagnetic neutrino follow-up programs, including the expected potential for the Rubin Observatory.

Large-scale perturbations in the microbiome constitution are strongly correlated, whether as a driver or a consequence, with the health and functioning of human physiology. However, understanding the difference in the microbiome profiles of healthy and ill individuals can be complicated due to the large number of complex interactions among microbes. We propose to model these interactions as a time-evolving graph whose nodes are microbes and edges are interactions among them. Motivated by the need to analyse such complex interactions, we develop a method that learns a low-dimensional representation of the time-evolving graph and maintains the dynamics occurring in the high-dimensional space. Through our experiments, we show that we can extract graph features such as clusters of nodes or edges that have the highest impact on the model to learn the low-dimensional representation. This information can be crucial to identify microbes and interactions among them that are strongly correlated with clinical diseases. We conduct our experiments on both synthetic and real-world microbiome datasets.

Let $G=(V,E)$ be an undirected unweighted planar graph. Consider a vector storing the distances from an arbitrary vertex $v$ to all vertices $S = \{ s_1 , s_2 , \ldots , s_k \}$ of a single face in their cyclic order. The pattern of $v$ is obtained by taking the difference between every pair of consecutive values of this vector. In STOC'19, Li and Parter used a VC-dimension argument to show that in planar graphs, the number of distinct patterns, denoted $x$, is only $O(k^3)$. This resulted in a simple compression scheme requiring $\tilde O(\min \{ k^4+|T|, k\cdot |T|\})$ space to encode the distances between $S$ and a subset of terminal vertices $T \subseteq V$. This is known as the Okamura-Seymour metric compression problem. We give an alternative proof of the $x=O(k^3)$ bound that exploits planarity beyond the VC-dimension argument. Namely, our proof relies on cut-cycle duality, as well as on the fact that distances among vertices of $S$ are bounded by $k$. Our method implies the following: (1) An $\tilde{O}(x+k+|T|)$ space compression of the Okamura-Seymour metric, thus improving the compression of Li and Parter to $\tilde O(\min \{k^3+|T|,k \cdot |T| \})$. (2) An optimal $\tilde{O}(k+|T|)$ space compression of the Okamura-Seymour metric, in the case where the vertices of $T$ induce a connected component in $G$. (3) A tight bound of $x = \Theta(k^2)$ for the family of Halin graphs, whereas the VC-dimension argument is limited to showing $x=O(k^3)$.

Given two strings $S$ and $P$, the Episode Matching problem is to find the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997) , where $n,m$ are the lengths of $S$ and $P$, respectively. Although the problem is well studied and has many applications in data mining, this bound has never been improved. In this paper we show why this is the case by proving that no $O((nm)^{1-\epsilon})$ algorithm (even for binary strings) exists, unless the Strong Exponential Time Hypothesis (SETH) is false. We then consider the indexing version of the problem, where $S$ is preprocessed into a data structure for answering episode matching queries $P$. We show that for any $\tau$, there is a data structure using $O(n+\left(\frac{n}{\tau}\right)^k)$ space that answers episode matching queries for any $P$ of length $k$ in $O(k\cdot \tau \cdot \log \log n )$ time. We complement this upper bound with an almost matching lower bound, showing that any data structure that answers episode matching queries for patterns of length $k$ in time $O(n^\delta)$, must use $\Omega(n^{k-k\delta-o(1)})$ space, unless the Strong $k$-Set Disjointness Conjecture is false. Finally, for the special case of $k=2$, we present a faster construction of the data structure using fast min-plus multiplication of bounded integer matrices., Comment: This is the full version of a paper accepted to CPM 2022

1) The local environment and land usages have changed a lot during the past one hundred years. Historical documents and materials are crucial in understanding and following these changes. Historical documents are, therefore, an important piece in the understanding of the impact and consequences of land usage change. This, in turn, is important in the search of restoration projects that can be conducted to turn and reduce harmful and unsustainable effects originating from changes in the land-usage. 2) This work extracts information on the historical location and geographical distribution of wetlands, from hand-drawn maps. This is achieved by using deep learning (DL), and more specifically a convolutional neural network (CNN). The CNN model is trained on a manually pre-labelled dataset on historical wetlands in the area of J\"onk\"oping county in Sweden. These are all extracted from the historical map called "Generalstabskartan". 3) The presented CNN performs well and achieves a $F_1$-score of 0.886 when evaluated using a 10-fold cross validation over the data. The trained models are additionally used to generate a GIS layer of the presumable historical geographical distribution of wetlands for the area that is depicted in the southern collection in Generalstabskartan, which covers the southern half of Sweden. This GIS layer is released as an open resource and can be freely used. 4) To summarise, the presented results show that CNNs can be a useful tool in the extraction and digitalisation of non-textual information in historical documents, such as historical maps. A modern GIS material that can be used to further understand the past land-usage change is produced within this research.