Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data. Our proposed method directly learns the missing values in a bidirectional recurrent dynamical system, without any specific assumption. The imputed values are treated as variables of RNN graph and can be effectively updated during the backpropagation.BRITS has three advantages: (a) it can handle multiple correlated missing values in time series; (b) it generalizes to time series with nonlinear dynamics underlying; (c) it provides a data-driven imputation procedure and applies to general settings with missing data.We evaluate our model on three real-world datasets, including an air quality dataset, a health-care data, and a localization data for human activity.
Phylogenetic networks generalize phylogenetic trees to evolutionary histories that include reticulate events such as recombination, horizontal gene transfer, and hybridization. Under a Markov model of nucleotide substitution, a phylogenetic network determines a distribution of leaf-patterns. Here, we study the identifiability of the network topology from this distribution under the Jukes-Cantor (JC), Kimura 2-parameter (K2P), and Kimura 3-parameter (K3P) models. Our first result is that the semi-directed network parameter of a level-1 phylogenetic network (modulo redirecting triangles) is fully identifiable under all three models, on a biologically reasonable parameter space in which substitution rates are probabilistic and mixing parameters are non-trivial (i.e., not 0 or 1). In contrast to the generic identifiability established in prior work, this holds at every point of the parameter space, not merely off of a measure-zero subset. Our second result distinguishes phylogenetic networks from phylogenetic trees, on the same parameter space, under JC and K2P. We prove that no phylogenetic network and phylogenetic tree can induce the same leaf-pattern distribution unless the network
Incomplete sensor data is a major obstacle in industrial time-series analytics. In wastewater treatment plants (WWTPs), key sensors show long, irregular gaps caused by fouling, maintenance, and outages. We introduce STDiff and STDiff-W, diffusion-based imputers that cast gap filling as state-space simulation under partial observability, where targets, controls, and exogenous signals may all be intermittently missing. STDiff learns a one-step transition model conditioned on observed values and masks, while STDiff-W extends this with a context encoder that jointly inpaints contiguous blocks, combining long-range consistency with short-term detail. On two WWTP datasets (one with synthetic block gaps from Agtrup and another with natural outages from Avedøre), STDiff-W achieves state-of-the-art accuracy compared with strong neural baselines such as SAITS, BRITS, and CSDI. Beyond point-error metrics, its reconstructions preserve realistic dynamics including oscillations, spikes, and regime shifts, and they achieve top or tied-top downstream one-step forecasting performance compared with strong neural baselines, indicating that preserving dynamics does not come at the expense of predictiv
Retrieval-Augmented Generation (RAG) has emerged as a promising technique to enhance the quality and relevance of responses generated by large language models. While recent advancements have mainly focused on improving RAG for text-based queries, RAG on multi-modal documents containing both texts and images has not been fully explored. Especially when fine-tuning does not work. This paper proposes BRIT, a novel multi-modal RAG framework that effectively unifies various text-image connections in the document into a multi-modal graph and retrieves the texts and images as a query-specific sub-graph. By traversing both image-to-text and text-to-image paths in the graph, BRIT retrieve not only directly query-relevant images and texts but also further relevant contents to answering complex cross-modal multi-hop questions. To evaluate the effectiveness of BRIT, we introduce MM-RAG test set specifically designed for multi-modal question answering tasks that require to understand the text-image relations. Our comprehensive experiments demonstrate the superiority of BRIT, highlighting its ability to handle cross-modal questions on the multi-modal documents.
Many philosophers of physics maintain that a physical theory that exhibits (certain kinds of) symmetries is flawed, on the grounds that such theories posit "excess structure". In an influential paper, Dewar [2019, "Sophistication about Symmetries", \emph{Brit. J. Phil. Sci.} \textbf{70}: 485-521] introduces a distinction between "reduction" and "sophistication" as alternative ways of removing excess structure. In this paper we re-examine the distinction as Dewar draws it, and we argue that there is no physically or philosophically important distinction between what Dewar calls "reduction" and what he calls "internal sophistication". We then argue that there are multiple notions of "reduction" in the literature that ought to be distinguished, both in motivation and in outcome.
We prove, for Hermitian algebras, the multiplicative version of the Kowalski-Słodkowski Theorem which identifies the characters among the collection of all complex valued functions on a Banach algebra $A$ in terms of a spectral condition. Specifically, we show that, if $A$ is a Hermitian algebra, and if $φ:A\mapsto\mathbb C$ is a continuous function satisfying $φ(x)φ(y) \in σ(xy)$ for all $x,y\in A$ (where $σ$ denotes the spectrum), then either $φ$ or $-φ$ is a character of $A$; of course the converse holds as well. Our proof depends fundamentally on the existence of positive elements and square roots in these algebras.
Healthcare time series data is vital for monitoring patient activity but often contains noise and missing values due to various reasons such as sensor errors or data interruptions. Imputation, i.e., filling in the missing values, is a common way to deal with this issue. In this study, we compare imputation methods, including Multiple Imputation with Random Forest (MICE-RF) and advanced deep learning approaches (SAITS, BRITS, Transformer) for noisy, missing time series data in terms of MAE, F1-score, AUC, and MCC, across missing data rates (10 % - 80 %). Our results show that MICE-RF can effectively impute missing data compared to deep learning methods and the improvement in classification of data imputed indicates that imputation can have denoising effects. Therefore, using an imputation algorithm on time series with missing data can, at the same time, offer denoising effects.
For a semisimple unital Banach algebra $A$ over $\mathbb{C}$, and elements $a,b\in A,$ we show that the similarity orbits, $\mathrm{orb}(a)$ and $\mathrm{orb}(b)$, over the principal component of the invertible group of $A$ commute precisely when there is at least one nonzero complex number not belonging to the spectrum of any product $a^\prime b^\prime$ -- where $(a^\prime,b^\prime)\in\mathrm{orb}(a)\times\mathrm{orb}(b)$. In this case, the polynomially convex hull of the spectra of the $a^\prime b^\prime$ is constant. When $\mathrm{orb}(a)=\mathrm{orb}(b)$, then $a$ is central under the aforementioned assumption -- and the result then generalizes part of an old theorem due to J. Zemánek. We show further that the two classical characterizations of commutative Banach algebras via the spectral radius can be algebraically localized in the sense of `local' implies `global'. Thereafter, in Section 3, we give a (somewhat weaker) localization of the above situation involving spectral perturbation on small neighborhoods in a similarity orbit. Finally, we apply the above results to algebraic elements and idempotents in particular, so that orthogonality of similarity orbits of two idempoten
We establish some Lie--Trotter formulae for unital complex Jordan--Banach algebras, showing that for each couple of elements $a,b$ in a unital complex Jordan--Banach algebra $\mathfrak{A}$ the identities $$ \lim_{n\to \infty} \left(e^{\frac{a}{n}}\circ e^{\frac{b}{n}} \right)^{n} = e^{a+b},\ \lim_{n\to \infty} \left(U_{e^{\frac{a}{n}}} \left( e^{\frac{b}{n}}\right) \right)^{n} = e^{2 a+b}, \hbox{ and }$$ $$ \lim_{n\to \infty} \left(U_{e^{\frac{a}{n}},e^{\frac{c}{n}}} \left( e^{\frac{b}{n}}\right) \right)^{n} = e^{a+b + c}$$ hold. These formulae are actually deduced from a more general result involving holomorphic functions with values in $\mathfrak{A}$. These formulae are employed in the study of spectral-valued (non-necessarily linear) functionals $f:\mathfrak{A}\to \mathbb{C}$ satisfying $f(U_x (y))=U_{f(x)}f(y),$ for all $x,y\in \mathfrak{A}$. We prove that for any such a functional $f,$ there exists a unique continuous (Jordan-)multiplicative linear functional $ψ\colon \mathfrak{A}\to\mathbb{C}$ such that $ f(x)=ψ(x),$ for every $x$ in the connected component of set of all invertible elements of $\mathfrak{A}$ containing the unit element. If we additionally assume that $\mathfr
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