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Deceptive reviews are becoming increasingly common, especially given the increase in performance and the prevalence of LLMs. While work to date has addressed the development of models to differentiate between truthful and deceptive human reviews, much less is known about the distinction between real reviews and AI-authored fake reviews. Moreover, most of the research so far has focused primarily on English, with very little work dedicated to other languages. In this paper, we compile and make publicly available the MAiDE-up dataset, consisting of 10,000 real and 10,000 AI-generated fake hotel reviews, balanced across ten languages. Using this dataset, we conduct extensive linguistic analyses to (1) compare the AI fake hotel reviews to real hotel reviews, and (2) identify the factors that influence the deception detection model performance. We explore the effectiveness of several models for deception detection in hotel reviews across three main dimensions: sentiment, location, and language. We find that these dimensions influence how well we can detect AI-generated fake reviews.

We consider an $n\times n$ system of ODEs on $\mathbb{P}^1$ with a simple pole $A$ at $z=0$ and a double pole $u={\rm diag}(u_1, \dots, u_n)$ at $z=\infty$. This is the simplest situation in which the monodromy data of the system are described by upper and lower triangular Stokes matrices $S_\pm$, and we impose reality conditions which imply $S_-=S_+^\dagger$. We study leading WKB exponents of Stokes matrices in parametrizations given by generalized minors and by spectral coordinates, and we show that for $u$ on the caterpillar line (which corresponds to the limit $(u_{j+1}-u_j)/(u_j - u_{j-1}) \to \infty$ for $j=2, \cdots, n-1$), the real parts of these exponents are given by periods of certain cycles on the degenerate spectral curve $\Gamma(u_{\rm cat}(t), A)$. These cycles admit unique deformations for $u$ near the caterpillar line. Using the spectral network theory, we give for $n=2$, and $n=3$ exact WKB predictions for asymptotics of generalized minors in terms of periods of these cycles. Boalch's theorem from Poisson geometry implies that real parts of leading WKB exponents satisfy the rhombus (or interlacing) inequalities. We show that these inequalities are in correspondence with finite webs of the canonical foliation on the root curve $\Gamma^r(u, A)$, and that they follow from the positivity of the corresponding periods. We conjecture that a similar mechanism applies for $n>3$. We also outline the relation of the spectral coordinates with the cluster structures considered by Goncharov-Shen, and with ${\mathcal N}=2$ supersymmetric quantum field theories in dimension four associated with some simple quivers.

We present Dynamics-Guided Diffusion Model, a data-driven framework for generating manipulator geometry designs for a given manipulation task. Instead of training different design models for each task, our approach employs a learned dynamics network shared across tasks. For a new manipulation task, we first decompose it into a collection of individual motion targets which we call target interaction profile, where each individual motion can be modeled by the shared dynamics network. The design objective constructed from the target and predicted interaction profiles provides a gradient to guide the refinement of finger geometry for the task. This refinement process is executed as a classifier-guided diffusion process, where the design objective acts as the classifier guidance. We evaluate our framework on various manipulation tasks, under the sensor-less setting using only an open-loop parallel jaw motion. Our generated designs outperform optimization-based and unguided diffusion baselines relatively by 31.5% and 45.3% on average manipulation success rate. With the ability to generate a design within 0.8 seconds, our framework could facilitate rapid design iteration and enhance the adoption of data-driven approaches for robotic mechanism design.

In this article, we study a special class of Jimbo-Miwa-Mori-Sato isomonodromy equations, which can be seen as a higher-dimensional generalization of Painlev\'e VI. We first construct its convergent $n\times n$ matrix series solutions satisfying certain boundary condition. We then use the Riemann-Hilbert approach to prove that the resulting solutions are almost all the solutions. Along the way, we find a shrinking phenomenon of the eigenvalues of the submatrices of the generic matrix solutions in the long time behaviour., Comment: 46 pages, 1 figures

In this paper, we first give a new interpretation of Jimbo's boundary condition for the generic Painlev\'e VI transcendents, as the shrinking phenomenon in long time behaviour of the Jimbo-Miwa-Mori-Sato equation with rank $n=3$. We then interpret Jimbo's monodromy formula from the viewpoint of the isomonodromy deformation with respect to irregular singularities., Comment: 22 pages

In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincar\'e rank one. The sources of the interests in the Stokes phenomenon of such system are from representation theory and the theory of isomonodromy deformation., Comment: 29 pages

The Alekseev-Meinrenken diffeomorphism is a distinguished diffeomorphism from the space of $n\times n$ Hermitian matrices to the space of $n\times n$ positive definite Hermitian matrices. This paper derives the explicit expression of the diffeomorphism, via the Stokes phenomenon of meromorphic linear systems of ordinary differential equations with Poncar\'{e} rank $1$., Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:1912.07196

We propose a method that trains a neural radiance field (NeRF) to encode not only the appearance of the scene but also semantic correlations between scene points, regions, or entities -- aiming to capture their mutual co-variation patterns. In contrast to the traditional first-order photometric reconstruction objective, our method explicitly regularizes the learning dynamics to align the Jacobians of highly-correlated entities, which proves to maximize the mutual information between them under random scene perturbations. By paying attention to this second-order information, we can shape a NeRF to express semantically meaningful synergies when the network weights are changed by a delta along the gradient of a single entity, region, or even a point. To demonstrate the merit of this mutual information modeling, we leverage the coordinated behavior of scene entities that emerges from our shaping to perform label propagation for semantic and instance segmentation. Our experiments show that a JacobiNeRF is more efficient in propagating annotations among 2D pixels and 3D points compared to NeRFs without mutual information shaping, especially in extremely sparse label regimes -- thus reducing annotation burden. The same machinery can further be used for entity selection or scene modifications.

When manipulating an object to accomplish complex tasks, humans rely on both vision and touch to keep track of the object's 6D pose. However, most existing object pose tracking systems in robotics rely exclusively on visual signals, which hinder a robot's ability to manipulate objects effectively. To address this limitation, we introduce TEG-Track, a tactile-enhanced 6D pose tracking system that can track previously unseen objects held in hand. From consecutive tactile signals, TEG-Track optimizes object velocities from marker flows when slippage does not occur, or regresses velocities using a slippage estimation network when slippage is detected. The estimated object velocities are integrated into a geometric-kinematic optimization scheme to enhance existing visual pose trackers. To evaluate our method and to facilitate future research, we construct a real-world dataset for visual-tactile in-hand object pose tracking. Experimental results demonstrate that TEG-Track consistently enhances state-of-the-art generalizable 6D pose trackers in synthetic and real-world scenarios. Our code and dataset are available at https://github.com/leolyliu/TEG-Track.

Training a generalizable 3D part segmentation network is quite challenging but of great importance in real-world applications. To tackle this problem, some works design task-specific solutions by translating human understanding of the task to machine's learning process, which faces the risk of missing the optimal strategy since machines do not necessarily understand in the exact human way. Others try to use conventional task-agnostic approaches designed for domain generalization problems with no task prior knowledge considered. To solve the above issues, we propose AutoGPart, a generic method enabling training generalizable 3D part segmentation networks with the task prior considered. AutoGPart builds a supervision space with geometric prior knowledge encoded, and lets the machine to search for the optimal supervisions from the space for a specific segmentation task automatically. Extensive experiments on three generalizable 3D part segmentation tasks are conducted to demonstrate the effectiveness and versatility of AutoGPart. We demonstrate that the performance of segmentation networks using simple backbones can be significantly improved when trained with supervisions searched by our method., Comment: 22 pages, CVPR 2022

In this paper, we derive the connection formula for the higher rank analog of Painlev\'{e} VI arising from the isomonodromic deformation theory and the study of Frobenius manifolds., Comment: 9 pages

In this paper, we give a complex analysis realization of $\frak{gl}_n$-crystals and their tensor products. Motivated by this, we propose that the WKB approximation of the Stokes matrices, of certain meromorphic linear systems of ordinary differential equations, is characterized by $\frak{gl}_n$-crystal structures on the eigenbasis of shift of argument subalgebras of the universal enveloping algebra $U({\frak {gl}}_n)$., Comment: arXiv admin note: substantial text overlap with arXiv:1912.07196

In this paper we prove that the quantum Stokes matrices of the quantum differential equation at a second order pole give rise to representations of the quantum group $U_q(\frak{gl}_n)$. We explain our results from the viewpoint of deformation quantization of the classical Stokes matrices at a second order pole. As a consequence, we can get a dictionary between the theory of Stokes phenomenon and the theory of quantum groups. We briefly discuss several such correspondences, and outline the generalization of our results to all classical types of Lie algebras and to the quantum differential equation at an arbitrary order pole., Comment: 45 pages

In this paper, we study the Stokes phenomenon of the cyclotomic Knizhnik-Zamolodchikov equation, and prove that its two types of Stokes matrices satisfy the Yang-Baxter and reflection equations respectively. We then discuss its isomonodromy deformation, and its relations with cyclotomic associators, twists, and quantum symmetric pairs., Comment: 16 pages

In the first part of the paper, we solve the boundary and monodromy problems for the isomonodromy equation of the $n\times n$ meromorphic linear system of ordinary differential equations with Poncar\'{e} rank $1$. In particular, we derive an explicit expression of the Stokes matrices of the linear system, via the boundary value of the solutions of the isomonodromy equation at a critical point. Motivated by this result, we then describe the regularized limits of Stokes matrices as the irregular data $u={\rm diag}(u_1,...,u_n)$ in the linear system degenerates, i.e., as some $u_i, u_j,...,u_k$ collapse. The prescription of the regularized limit is controlled by the geometry of the De Concini-Procesi wonderful compactification space. As applications, many analysis problems about higher rank Painlev\'e transcendents can be solved. In the second part of the paper, we show some important applications of the above analysis results in representation theory and Poisson geometry: we obtain the first transcendental realization of crystals in representations of $\frak{gl}_n$ via the Stokes phenomenon in the WKB approximation; we develop a wall-crossing formula that characterizes the discontinuous jump of the regularized limits of Stokes matrices as crossing walls in the compactification space, and interpret the known cactus group actions on crystals arising from representation theory as a wall-crossing phenomenon; and we find the first explicit linearization of the standard dual Poisson Lie group for $U(n)$., Comment: 80 pages

The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 were computed by Feigin and Veselov [Int. Math. Res. Not. 2002 (2002), 521-545]. In this paper, we show some partial results and make two conjectures on the Hilbert series of these spaces over fields of positive characteristic. On the other hand, Braverman, Etingof and Finkelberg [arXiv:1611.10216] introduced the spaces of quasi-invariant polynomials twisted by a monomial. We extend some of their results to the spaces twisted by a smooth function.