Rationally designed α-conotoxin analogues maintained analgesia activity and weakened side effects

A lack of specificity is restricting the further application of conotoxin from Conus bullatus (BuIA). In this study, an analogue library of BuIA was established and virtual screening was used, which identified high α7 nicotinic acetylcholine receptor (nAChR)-selectivity analogues. The analogues were synthesized and tested for their affinity to functional human α7 nAChR and for the regulation of intracellular calcium ion capacity in neurons. Immunofluorescence, flow cytometry, and patch clamp results showed that the analogues maintained their capacity for calcium regulation. The results of the hot-plate model and paclitaxel-induced peripheral neuropathy model indicated that, when compared with natural BuIA, the analgesia activities of the analogues in different models were maintained. To analyze the adverse effects and toxicity of BuIA and its analogues, the tail suspension test, forced swimming test, and open field test were used. The results showed that the safety and toxicity of the analogues were significantly better than BuIA. The analogues of BuIA with an appropriate and rational mutation showed high selectivity and maintained the regulation of Ca2+ capacity in neurons and activities of analgesia, whereas the analogues demonstrated that the adverse effects of natural α-conotoxins could be reduced

Geometric Phase-Driven Scattering Evolutions

Conventional approaches for scattering manipulations rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is non-generic (expansion coefficients depend on the position of the coordinate system's origin) and more descriptive than predictive. Here we explore this classical topic from a different perspective of controlled excitations and interferences of quasi-normal modes (QNMs) supported by the scattering system. Scattered waves are expanded into not spherical harmonics but radiations of QNMs, among which the relative amplitudes and phases are crucial factors to architect for scattering manipulations. Relying on the electromagnetic reciprocity, we provide full geometric representations based on the Poincar\'e sphere for those factors, and identify the hidden underlying geometric phases of QNMs that drive the scattering evolutions. Further synchronous exploitations of the incident polarization-dependent geometric phases and excitation amplitudes enable efficient manipulations of both scattering intensities and polarizations. Continuous geometric phase spanning $2\pi$ is directly manifest through scattering variations, even in the rather elementary configuration of an individual particle scattering waves of varying polarizations. We have essentially established a profoundly all-encompassing framework for the calculations of geometric phase in scattering systems, which will greatly broaden horizons of many disciplines not only in photonics but also in general wave physics where geometric phase is generic and ubiquitous.Comment: Wei Liu acknowledges many illuminating correspondences with Sir Michael Berry, whose monumental paper on geometric phase was published 40 years ago toda

Distributed Invariant Kalman Filter for Cooperative Localization using Matrix Lie Groups

This paper studies the problem of Cooperative Localization (CL) for multi-robot systems, where a group of mobile robots jointly localize themselves by using measurements from onboard sensors and shared information from other robots. We propose a novel distributed invariant Kalman Filter (DInEKF) based on the Lie group theory, to solve the CL problem in a 3-D environment. Unlike the standard EKF which computes the Jacobians based on the linearization at the state estimate, DInEKF defines the robots' motion model on matrix Lie groups and offers the advantage of state estimate-independent Jacobians. This significantly improves the consistency of the estimator. Moreover, the proposed algorithm is fully distributed, relying solely on each robot's ego-motion measurements and information received from its one-hop communication neighbors. The effectiveness of the proposed algorithm is validated in both Monte-Carlo simulations and real-world experiments. The results show that the proposed DInEKF outperforms the standard distributed EKF in terms of both accuracy and consistency

Block Coordinate Descent Methods for Optimization under J-Orthogonality Constraints with Applications

The J-orthogonal matrix, also referred to as the hyperbolic orthogonal matrix, is a class of special orthogonal matrix in hyperbolic space, notable for its advantageous properties. These matrices are integral to optimization under J-orthogonal constraints, which have widespread applications in statistical learning and data science. However, addressing these problems is generally challenging due to their non-convex nature and the computational intensity of the constraints. Currently, algorithms for tackling these challenges are limited. This paper introduces JOBCD, a novel Block Coordinate Descent method designed to address optimizations with J-orthogonality constraints. We explore two specific variants of JOBCD: one based on a Gauss-Seidel strategy (GS-JOBCD), the other on a variance-reduced and Jacobi strategy (VR-J-JOBCD). Notably, leveraging the parallel framework of a Jacobi strategy, VR-J-JOBCD integrates variance reduction techniques to decrease oracle complexity in the minimization of finite-sum functions. For both GS-JOBCD and VR-J-JOBCD, we establish the oracle complexity under mild conditions and strong limit-point convergence results under the Kurdyka-Lojasiewicz inequality. To demonstrate the effectiveness of our method, we conduct experiments on hyperbolic eigenvalue problems, hyperbolic structural probe problems, and the ultrahyperbolic knowledge graph embedding problem. Extensive experiments using both real-world and synthetic data demonstrate that JOBCD consistently outperforms state-of-the-art solutions, by large margins

Time-Space Tradeoffs of Truncation with Preprocessing

Truncation of cryptographic outputs is a technique that was recently introduced in Baldimtsi et al. [BCCK22]. The general idea is to try out many inputs to some cryptographic algorithm until the output (e.g. a public-key or some hash value) falls into some sparse set and thus can be compressed: by trying out an expected $2^k$ different inputs one will find an output that starts with $k$ zeros. Using such truncation one can for example save substantial gas fees on Blockchains where storing values is very expensive. While [BCCK22] show that truncation preserves the security of the underlying primitive, they only consider a setting without preprocessing. In this work we show that lower bounds on the time-space tradeoff for inverting random functions and permutations also hold with truncation, except for parameters ranges where the bound fails to hold for \u27\u27trivial\u27\u27 reasons. Concretely, it\u27s known that any algorithm that inverts a random function or permutation with range $N$ making $T$ queries and using $S$ bits of auxiliary input must satisfy $S\cdot T\ge N\log N$. This lower bound no longer holds in the truncated setting where one must only invert a challenge from a range of size $N/2^k$, as now one can simply save the replies to all $N/2^k$ challenges, which requires $S=\log N\cdot N /2^k$ bits and allows to invert with $T=1$ query. We show that with truncation, whenever $S$ is somewhat smaller than the $\log N\cdot N /2^k$ bits required to store the entire truncated function table, the known $S\cdot T\ge N\log N$ lower bound applies

FORB: A Flat Object Retrieval Benchmark for Universal Image Embedding

Image retrieval is a fundamental task in computer vision. Despite recent advances in this field, many techniques have been evaluated on a limited number of domains, with a small number of instance categories. Notably, most existing works only consider domains like 3D landmarks, making it difficult to generalize the conclusions made by these works to other domains, e.g., logo and other 2D flat objects. To bridge this gap, we introduce a new dataset for benchmarking visual search methods on flat images with diverse patterns. Our flat object retrieval benchmark (FORB) supplements the commonly adopted 3D object domain, and more importantly, it serves as a testbed for assessing the image embedding quality on out-of-distribution domains. In this benchmark we investigate the retrieval accuracy of representative methods in terms of candidate ranks, as well as matching score margin, a viewpoint which is largely ignored by many works. Our experiments not only highlight the challenges and rich heterogeneity of FORB, but also reveal the hidden properties of different retrieval strategies. The proposed benchmark is a growing project and we expect to expand in both quantity and variety of objects. The dataset and supporting codes are available at https://github.com/pxiangwu/FORB/.Comment: NeurIPS 2023 Datasets and Benchmarks Trac

Robustness for Space-Bounded Statistical Zero Knowledge

We show that the space-bounded Statistical Zero Knowledge classes SZK_L and NISZK_L are surprisingly robust, in that the power of the verifier and simulator can be strengthened or weakened without affecting the resulting class. Coupled with other recent characterizations of these classes [Eric Allender et al., 2023], this can be viewed as lending support to the conjecture that these classes may coincide with the non-space-bounded classes SZK and NISZK, respectively

Unsupervised Contrast-Consistent Ranking with Language Models

Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank reviews by sentiment. Recent work focuses on pairwise, pointwise, and listwise prompting techniques to elicit a language model's ranking knowledge. However, we find that even with careful calibration and constrained decoding, prompting-based techniques may not always be self-consistent in the rankings they produce. This motivates us to explore an alternative approach that is inspired by an unsupervised probing method called Contrast-Consistent Search (CCS). The idea is to train a probing model guided by a logical constraint: a model's representation of a statement and its negation must be mapped to contrastive true-false poles consistently across multiple statements. We hypothesize that similar constraints apply to ranking tasks where all items are related via consistent pairwise or listwise comparisons. To this end, we extend the binary CCS method to Contrast-Consistent Ranking (CCR) by adapting existing ranking methods such as the Max-Margin Loss, Triplet Loss, and Ordinal Regression objective. Our results confirm that, for the same language model, CCR probing outperforms prompting and even performs on a par with prompting much larger language models