De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and repeating it over and over. In particular, the quantum de Finetti theorem says that exchangeable sequences of quantum states are always represented by distributions over a single state produced over and over. The main result of this paper is that this quantum de Finetti construction has a universal property as a categorical limit. This allows us to pass canonically between categorical treatments of finite dimensional quantum theory and the infinite dimensional. The treatment here is through understanding properties of (co)limits with respect to the contravariant functor which takes a C*-algebra describing a physical system to its convex, compact space of states, and through discussion of the Radon probability monad. We also show that the same categorical analysis also justifies a continuous de Finetti theorem for classical probability.
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Packet loss is a common and unavoidable problem in voice over internet phone (VoIP) systems. To deal with the problem, we propose a band-split packet loss concealment network (BS-PLCNet). Specifically, we split the full-band signal into wide-band (0-8kHz) and high-band (8-24kHz). The wide-band signals are processed by a gated convolutional recurrent network (GCRN), while the high-band counterpart is processed by a simple GRU network. To ensure high speech quality and automatic speech recognition (ASR) compatibility, multi-task learning (MTL) framework including fundamental frequency (f0) prediction, linguistic awareness, and multi-discriminators are used. The proposed approach tied for 1st place in the ICASSP 2024 PLC Challenge.
Bioinformatics and Computational Biology are two fields that have been exploiting GPUs for more than two decades, being CUDA the most used programming language for them. However, as CUDA is an NVIDIA proprietary language, it implies a strong portability restriction to a wide range of heterogeneous architectures, like AMD or Intel GPUs. To face this issue, the Khronos Group has recently proposed the SYCL standard, which is an open, royalty-free, cross-platform abstraction layer, that enables the programming of a heterogeneous system to be written using standard, single-source C++ code. Over the past few years, several implementations of this SYCL standard have emerged, being oneAPI the one from Intel. This paper presents the migration process of the SW\# suite, a biological sequence alignment tool developed in CUDA, to SYCL using Intel's oneAPI ecosystem. The experimental results show that SW\# was completely migrated with a small programmer intervention in terms of hand-coding. In addition, it was possible to port the migrated code between different architectures (considering multiple vendor GPUs and also CPUs), with no noticeable performance degradation on 5 different NVIDIA GPUs. Moreover, performance remained stable when switching to another SYCL implementation. As a consequence, SYCL and its implementations can offer attractive opportunities for the Bioinformatics community, especially considering the vast existence of CUDA-based legacy codes.
In this work, we study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method for approximating the Koopman operator associated with an unknown nonlinear dynamical system from discrete-time snapshots, while preserving the self-adjointness of the operator on its finite-dimensional approximations. We show that, under suitable conditions, the eigenvalues and eigenfunctions of HDMD converge to the spectral properties of the underlying Koopman operator. Along the way, we establish a general theorem on the convergence of spectral measures, and demonstrate our results numerically on the two-dimensional Schr\"odinger equation.
Intelligent metasurfaces are one of the favorite technologies for integrating sixth-generation (6G) networks, especially the reconfigurable intelligent surface (RIS) that has been extensively researched in various applications. In this context, a feature that deserves further exploration is the frequency scattering that occurs when the elements are periodically switched, referred to as Space-Time-Coding metasurface (STCM) topology. This type of topology causes impairments to the established communication methods by generating undesirable interference both in frequency and space, which is worsened when using wideband signals. Nevertheless, it has the potential to bring forward useful features for sensing and localization. This work exploits STCM sensing capabilities in target detection, localization, and classification using narrowband downlink pilot signals at the base station (BS). The results of this novel approach reveal the ability to retrieve a scattering point (SP) localization within the sub-centimeter and sub-decimeter accuracy depending on the SP position in space. We also analyze the associated detection and classification probabilities, which show reliable detection performance in the whole analyzed environment. In contrast, the classification is bounded by physical constraints, and we conclude that this method presents a promising approach for future integrated sensing and communications (ISAC) protocols by providing a tool to perform sensing and localization services using legacy communication signals.
Defeasibility in causal reasoning implies that the causal relationship between cause and effect can be strengthened or weakened. Namely, the causal strength between cause and effect should increase or decrease with the incorporation of strengthening arguments (supporters) or weakening arguments (defeaters), respectively. However, existing works ignore defeasibility in causal reasoning and fail to evaluate existing causal strength metrics in defeasible settings. In this work, we present {\delta}-CAUSAL, the first benchmark dataset for studying defeasibility in causal reasoning. {\delta}-CAUSAL includes around 11K events spanning ten domains, featuring defeasible causality pairs, i.e., cause-effect pairs accompanied by supporters and defeaters. We further show current causal strength metrics fail to reflect the change of causal strength with the incorporation of supporters or defeaters in {\delta}-CAUSAL. To this end, we propose CESAR (Causal Embedding aSsociation with Attention Rating), a metric that measures causal strength based on token-level causal relationships. CESAR achieves a significant 69.7% relative improvement over existing metrics, increasing from 47.2% to 80.1% in capturing the causal strength change brought by supporters and defeaters. We further demonstrate even Large Language Models (LLMs) like GPT-3.5 still lag 4.5 and 10.7 points behind humans in generating supporters and defeaters, emphasizing the challenge posed by {\delta}-CAUSAL.
Knowing who follows whom and what patterns they are following are crucial steps to understand collective behaviors (e.g. a group of human, a school of fish, or a stock market). Time series is one of resources that can be used to get insight regarding following relations. However, the concept of following patterns or motifs and the solution to find them in time series are not obvious. In this work, we formalize a concept of following motifs between two time series and present a framework to infer following patterns between two time series. The framework utilizes one of efficient and scalable methods to retrieve motifs from time series called the Matrix Profile Method. We compare our proposed framework with several baselines. The framework performs better than baselines in the simulation datasets. In the dataset of sound recording, the framework is able to retrieve the following motifs within a pair of time series that two singers sing following each other. In the cryptocurrency dataset, the framework is capable of capturing the following motifs within a pair of time series from two digital currencies, which implies that the values of one currency follow the values of another currency patterns. Our framework can be utilized in any field of time series to get insight regarding following patterns between time series.
Observers for PDEs are themselves PDEs. Therefore, producing real time estimates with such observers is computationally burdensome. For both finite-dimensional and ODE systems, moving-horizon estimators (MHE) are operators whose output is the state estimate, while their inputs are the initial state estimate at the beginning of the horizon as well as the measured output and input signals over the moving time horizon. In this paper we introduce MHEs for PDEs which remove the need for a numerical solution of an observer PDE in real time. We accomplish this using the PDE backstepping method which, for certain classes of both hyperbolic and parabolic PDEs, produces moving-horizon state estimates explicitly. Precisely, to explicitly produce the state estimates, we employ a backstepping transformation of a hard-to-solve observer PDE into a target observer PDE, which is explicitly solvable. The MHEs we propose are not new observer designs but simply the explicit MHE realizations, over a moving horizon of arbitrary length, of the existing backstepping observers. Our PDE MHEs lack the optimality of the MHEs that arose as duals of MPC, but they are given explicitly, even for PDEs. In the paper we provide explicit formulae for MHEs for both hyperbolic and parabolic PDEs, as well as simulation results that illustrate theoretically guaranteed convergence of the MHEs.
In this paper, we conduct rigorous error analysis of the Lie-Totter time-splitting Fourier spectral scheme for the nonlinear Schr\"odinger equation with a logarithmic nonlinear term $f(u)=u\ln|u|^2$ (LogSE) and periodic boundary conditions on a $d$-dimensional torus $\mathbb T^d$. Different from existing works based on regularisation of the nonlinear term $ f(u)\approx f^\varepsilon(u)=u\ln (|u| + \varepsilon )^2,$ we directly discretize the LogSE with the understanding $f(0)=0.$ Remarkably, in the time-splitting scheme, the solution flow map of the nonlinear part: $g(u)= u {\rm e}^{-{\rm} i t \ln|u|^{2}}$ has a higher regularity than $f(u)$ (which is not differentiable at $u=0$ but H\"older continuous), where $g(u)$ is Lipschitz continuous and possesses a certain fractional Sobolev regularity with index $0<s<1$. Accordingly, we can derive the $L^2$-error estimate: $O\big((\tau^{s/2} + N^{-s})\ln\! N\big)$ of the proposed scheme for the LogSE with low regularity solution $u\in C((0,T]; H^s( \mathbb{T}^d)\cap L^\infty( \mathbb{T}^d)).$ Moreover, we can show that the estimate holds for $s=1$ with more delicate analysis of the nonlinear term and the associated solution flow maps. Furthermore, we provide ample numerical results to demonstrate such a fractional-order convergence for initial data with low regularity. This work is the first one devoted to the analysis of splitting scheme for the LogSE without regularisation in the low regularity setting, as far as we can tell.
Despite Multi-modal Large Language Models (MM-LLMs) have made exciting strides recently, they are still struggling to efficiently model the interactions among multi-modal inputs and the generation in non-textual modalities. In this work, we propose TEAL (Tokenize and Embed ALl)}, an approach to treat the input from any modality as a token sequence and learn a joint embedding space for all modalities. Specifically, for the input from any modality, TEAL first discretizes it into a token sequence with the off-the-shelf tokenizer and embeds the token sequence into a joint embedding space with a learnable embedding matrix. MM-LLMs just need to predict the multi-modal tokens autoregressively as the textual LLMs do. Finally, the corresponding de-tokenizer is applied to generate the output in each modality based on the predicted token sequence. With the joint embedding space, TEAL enables the frozen LLMs to perform both understanding and generation tasks involving non-textual modalities, such as image and audio. Thus, the textual LLM can just work as an interface and maintain its high performance in textual understanding and generation. Experiments show that TEAL achieves substantial improvements in multi-modal understanding, and implements a simple scheme for multi-modal generations.
In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the class of parity graphs is word-representable. Further, we obtain a characteristic property by which the recomposition of comparability graphs is a comparability graph. Consequently, we also establish the permutation-representation number (prn) of the resulting comparability graph. We also introduce a subclass of comparability graphs, called prn-irreducible graphs. We provide a criterion such that the split recomposition of two prn-irreducible graphs is a comparability graph and determine the prn of the resultant graph.
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