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The logic of information flows (LIF) has recently been proposed as a general framework in the field of knowledge representation. In this framework, tasks of procedural nature can still be modeled in a declarative, logic-based fashion. In this paper, we focus on the task of query processing under limited access patterns, a well-studied problem in the database literature. We show that LIF is well-suited for modeling this task. Toward this goal, we introduce a variant of LIF called "forward" LIF (FLIF), in a first-order setting. FLIF takes a novel graph-navigational approach; it is an XPath-like language that nevertheless turns out to be equivalent to the "executable" fragment of first-order logic defined by Nash and Lud\"ascher. One can also classify the variables in FLIF expressions as inputs and outputs. Expressions where inputs and outputs are disjoint, referred to as io-disjoint FLIF expressions, allow a particularly transparent translation into algebraic query plans that respect the access limitations. Finally, we show that general FLIF expressions can always be put into io-disjoint form.

We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems. The unbounded nature of the generator poses significant challenges, rendering conventional analysis techniques for Hilbert-Schmidt operators ineffective. To overcome this, we introduce a novel framework based on the energy functional for these stochastic processes. Our approach integrates physical priors through an energy-based risk metric in both full and partial knowledge settings. We evaluate the statistical performance of a reduced-rank estimator in reproducing kernel Hilbert spaces (RKHS) in the partial knowledge setting. Notably, our approach provides learning bounds independent of the state space dimension and ensures non-spurious spectral estimation. Additionally, we elucidate how the distortion between the intrinsic energy-induced metric of the stochastic diffusion and the RKHS metric used for generator estimation impacts the spectral learning bounds.

Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem, which is yet to be satisfactorily solved, especially for the popular Gaussian HMM with heterogeneous covariance. In this paper, we propose a consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. Moreover, we show that the model selection problem of HMM includes the order selection problem of finite mixture models as a special case. We give rigorous proof of the consistency of the proposed marginal likelihood method and provide an efficient computation method for practical implementation. We numerically compare the proposed method with the Bayesian information criterion (BIC), demonstrating the effectiveness of the proposed marginal likelihood method.

We introduce and characterize the operational diversity order (ODO) in fading channels, as a proxy to the classical notion of diversity order at any arbitrary operational signal-to-noise ratio (SNR). Thanks to this definition, relevant insights are brought up in a number of cases: (i) We quantify that in line-of-sight scenarios an increased diversity order is attainable compared to that achieved asymptotically; (ii) this effect is attenuated, but still visible, in the presence of an additional dominant specular component; (iii) we confirm that the decay slope in Rayleigh product channels increases very slowly and never fully achieves unitary slope for finite values of SNR.

According to many researchers, conceptual model (CM) development is a hard task, and system requirements are difficult to collect, causing many miscommunication problems. CMs require more than modeling ability alone - they first require an understanding of the targeted domain that the model attempts to represent. Accordingly, a preconceptual modeling (pre-CM) stage is intended to address ontological issues before typical CM development is initiated. It involves defining a portion of reality when entities and processes are differentiated and integrated as unified wholes. This pre-CM phase forms the focus of research in this paper. The purpose is not show how to model; rather, it is to demonstrate how to establish a metaphysical basis of the involved portion of reality. To demonstrate such a venture, we employ the so-called thinging machine (TM) modeling that has been proposed as a high-level CM. A TM model integrates staticity and dynamism grounded in a fundamental construct called a thimac (things/machine). It involves two modes of reality, existence (events) and subsistence (regions - roughly, specifications of things and processes). Currently, the dominant approach in CM has evolved to limit its scope of application to develop ontological categorization (types of things). In the TM approach, pre-CM metaphysics is viewed as a part and parcel of CM itself. The general research problem is how to map TM constructs to what is out there in the targeted domain. Discussions involve the nature of thimacs (things and processes) and subsistence and existence as they are superimposed over each other in reality. Specifically, we make two claims, (a) the perceptibility of regions as a phenomenon and (b) the distinctiveness of existence as a construct for events. The results contribute to further the understanding of TM modeling in addition to introducing some metaphysical insights.

The Method of Successive Approximations (MSA) is a fixed-point iterative method used to solve stochastic optimal control problems. It is an indirect method based on the conditions derived from the Stochastic Maximum Principle (SMP), an extension of the Pontryagin Maximum Principle (PMP) to stochastic control problems. In this study, we investigate the contractivity and the convergence of MSA for a specific and interesting class of stochastic dynamical systems (when the drift coefficient is one-sided-Lipschitz with a negative constant and the diffusion coefficient is Lipschitz continuous). Our analysis unfolds in three key steps: firstly, we prove the stability of the state process with respect to the control process. Secondly, we establish the stability of the adjoint process. Finally, we present rigorous evidence to prove the contractivity and then the convergence of MSA. This study contributes to enhancing the understanding of MSA's applicability and effectiveness in addressing stochastic optimal control problems.

Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively studied, where the fractures are treated as co-dimension one manifolds in a bulk matrix with low-dimensional governing equations. In this paper, we propose a simple yet effective treatment for modeling the fractures on fitted grids in the interior penalty discontinuous Galerkin (IPDG) methods without introducing any additional degrees of freedom or equations on the interfaces. We conduct stability and {\em hp}-analysis for the proposed IPDG method, deriving optimal a priori error bounds concerning mesh size ($h$) and sub-optimal bounds for polynomial degree ($k$) in both the energy norm and the $L^2$ norm. Numerical experiments involving published benchmarks validate our theoretical analysis and demonstrate the method's robust performance. Furthermore, we extend our method to two-phase flows and use numerical tests to confirm the algorithm's validity.

While large language models (LLMs) have demonstrated remarkable capabilities across a range of downstream tasks, a significant concern revolves around their propensity to exhibit hallucinations: LLMs occasionally generate content that diverges from the user input, contradicts previously generated context, or misaligns with established world knowledge. This phenomenon poses a substantial challenge to the reliability of LLMs in real-world scenarios. In this paper, we survey recent efforts on the detection, explanation, and mitigation of hallucination, with an emphasis on the unique challenges posed by LLMs. We present taxonomies of the LLM hallucination phenomena and evaluation benchmarks, analyze existing approaches aiming at mitigating LLM hallucination, and discuss potential directions for future research.

The advent of large language models marks a revolutionary breakthrough in artificial intelligence. With the unprecedented scale of training and model parameters, the capability of large language models has been dramatically improved, leading to human-like performances in understanding, language synthesizing, and common-sense reasoning, etc. Such a major leap-forward in general AI capacity will change the pattern of how personalization is conducted. For one thing, it will reform the way of interaction between humans and personalization systems. Instead of being a passive medium of information filtering, large language models present the foundation for active user engagement. On top of such a new foundation, user requests can be proactively explored, and user's required information can be delivered in a natural and explainable way. For another thing, it will also considerably expand the scope of personalization, making it grow from the sole function of collecting personalized information to the compound function of providing personalized services. By leveraging large language models as general-purpose interface, the personalization systems may compile user requests into plans, calls the functions of external tools to execute the plans, and integrate the tools' outputs to complete the end-to-end personalization tasks. Today, large language models are still being developed, whereas the application in personalization is largely unexplored. Therefore, we consider it to be the right time to review the challenges in personalization and the opportunities to address them with LLMs. In particular, we dedicate this perspective paper to the discussion of the following aspects: the development and challenges for the existing personalization system, the newly emerged capabilities of large language models, and the potential ways of making use of large language models for personalization.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.