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To analyze the worst-case running time of branching algorithms, the majority of work in exponential time algorithms focuses on designing complicated branching rules over developing better analysis methods for simple algorithms. In the mid-$2000$s, Fomin et al. [2005] introduced measure & conquer, an advanced general analysis method, sparking widespread adoption for obtaining tighter worst-case running time upper bounds for many fundamental NP-complete problems. Yet, much potential in this direction remains untapped, as most subsequent work applied it without further advancement. Motivated by this, we present piecewise analysis, a new general method that analyzes the running time of branching algorithms. Our approach is to define a similarity ratio that divides instances into groups and then analyze the running time within each group separately. The similarity ratio is a scale between two parameters of an instance I. Instead of relying on a single measure and a single analysis for the whole instance space, our method allows to take advantage of different intrinsic properties of instances with different similarity ratios. To showcase its potential, we reanalyze two $17$-year-old algorithms from Fomin et al. [2007] that solve $4$-Coloring and #$3$-Coloring respectively. The original analysis in their paper gave running times of $O(1.7272^n)$ and $O(1.6262^n)$ respectively for these algorithms, our analysis improves these running times to $O(1.7215^n)$ and $O(1.6232^n)$. Among the two improvements, our new running time $O(1.7215^n)$ is the first improvement in the best known running time for the 4-Coloring problem since 2007.

Controlling continuous-time dynamical systems is generally a two step process: first, identify or model the system dynamics with differential equations, then, minimize the control objectives to achieve optimal control function and optimal state trajectories. However, any inaccuracy in dynamics modeling will lead to sub-optimality in the resulting control function. To address this, we propose a neural ODE based method for controlling unknown dynamical systems, denoted as Neural Control (NC), which combines dynamics identification and optimal control learning using a coupled neural ODE. Through an intriguing interplay between the two neural networks in coupled neural ODE structure, our model concurrently learns system dynamics as well as optimal controls that guides towards target states. Our experiments demonstrate the effectiveness of our model for learning optimal control of unknown dynamical systems. Codes available at //github.com/chichengmessi/neural_ode_control/tree/main

The utilization of synthetic data for fingerprint recognition has garnered increased attention due to its potential to alleviate privacy concerns surrounding sensitive biometric data. However, current methods for generating fingerprints have limitations in creating impressions of the same finger with useful intra-class variations. To tackle this challenge, we present GenPrint, a framework to produce fingerprint images of various types while maintaining identity and offering humanly understandable control over different appearance factors such as fingerprint class, acquisition type, sensor device, and quality level. Unlike previous fingerprint generation approaches, GenPrint is not confined to replicating style characteristics from the training dataset alone: it enables the generation of novel styles from unseen devices without requiring additional fine-tuning. To accomplish these objectives, we developed GenPrint using latent diffusion models with multimodal conditions (text and image) for consistent generation of style and identity. Our experiments leverage a variety of publicly available datasets for training and evaluation. Results demonstrate the benefits of GenPrint in terms of identity preservation, explainable control, and universality of generated images. Importantly, the GenPrint-generated images yield comparable or even superior accuracy to models trained solely on real data and further enhances performance when augmenting the diversity of existing real fingerprint datasets.

Blockchain technology ensures secure and trustworthy data flow between multiple participants on the chain, but interoperability of on-chain and off-chain data has always been a difficult problem that needs to be solved. To solve the problem that blockchain systems cannot access off-chain data, oracle is introduced. however, existing research mainly focuses on the consistency and integrity of data, but ignores the problem that oracle nodes may be externally attacked or provide false data for selfish motives, resulting in the unresolved problem of data accuracy. In this paper, we introduce a new decentralized testing architecture (DesTest) that aims to improve data accuracy. A blockchain oracle random secret testing mechanism is first proposed to enhance the monitoring and verification of nodes by introducing a dynamic anonymized question-verification committee. Based on this, a comprehensive evaluation incentive mechanism is designed to incentivize honest work performance by evaluating nodes based on their reputation scores. The simulation results show that we successfully reduced the discrete entropy value of the acquired data and the real value of the data by 61.4%.

Object detection is a mature problem in autonomous driving with pedestrian detection being one of the first deployed algorithms. It has been comprehensively studied in the literature. However, object detection is relatively less explored for fisheye cameras used for surround-view near field sensing. The standard bounding box representation fails in fisheye cameras due to heavy radial distortion, particularly in the periphery. To mitigate this, we explore extending the standard object detection output representation of bounding box. We design rotated bounding boxes, ellipse, generic polygon as polar arc/angle representations and define an instance segmentation mIOU metric to analyze these representations. The proposed model FisheyeDetNet with polygon outperforms others and achieves a mAP score of 49.5 % on Valeo fisheye surround-view dataset for automated driving applications. This dataset has 60K images captured from 4 surround-view cameras across Europe, North America and Asia. To the best of our knowledge, this is the first detailed study on object detection on fisheye cameras for autonomous driving scenarios.

Correlations between quantum theory and music theory - specifically between principles of quantum computing and musical harmony - can lead to new understandings and new methodologies for music theorists and composers. The quantum principle of superposition is shown to be closely related to different interpretations of musical meaning. Superposition is implemented directly in the authors' simulations of quantum computing, as applied in the decision-making processes of computer-generated music composition.

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

To comprehensively gauge the capacity of current models for complex reasoning, it is crucial to assess their step-by-step reasoning in a scalable manner. Established reference-based evaluation metrics rely on human-annotated reasoning chains as references to assess the model-derived chains. However, such "gold-standard" human-written reasoning chains may not be unique and their acquisition is often labor-intensive. Existing reference-free reasoning evaluation metrics, while eliminating the need for human-crafted reasoning chains as references, often require fine-tuning with human-derived chains before evaluation, complicating the process and questioning their adaptability to other datasets. To address these challenges, we harness GPT-4 to automatically evaluate reasoning chain quality, thereby removing the dependency on human-written reasoning chains for both model fine-tuning and evaluative purposes. Leveraging the Socratic method, we develop SocREval ({\bf Soc}ratic Method-Inspired {\bf R}easoning {\bf Eval}uation), a novel approach for prompt design in reference-free reasoning evaluation. Empirical results from four human annotated datasets reveal that SocREval significantly improves GPT-4's performance, surpassing existing reference-free and reference-based reasoning evaluation metrics. Beyond its demonstrated efficacy, SocREval, proves to be both cost-efficient and robust to prompt writing and example selection, as substantiated by our in-depth analysis.

The prevalence of digital media and evolving sociopolitical dynamics have significantly amplified the dissemination of hateful content. Existing studies mainly focus on classifying texts into binary categories, often overlooking the continuous spectrum of offensiveness and hatefulness inherent in the text. In this research, we present an extensive benchmark dataset for Amharic, comprising 8,258 tweets annotated for three distinct tasks: category classification, identification of hate targets, and rating offensiveness and hatefulness intensities. Our study highlights that a considerable majority of tweets belong to the less offensive and less hate intensity levels, underscoring the need for early interventions by stakeholders. The prevalence of ethnic and political hatred targets, with significant overlaps in our dataset, emphasizes the complex relationships within Ethiopia's sociopolitical landscape. We build classification and regression models and investigate the efficacy of models in handling these tasks. Our results reveal that hate and offensive speech can not be addressed by a simplistic binary classification, instead manifesting as variables across a continuous range of values. The Afro-XLMR-large model exhibits the best performances achieving F1-scores of 75.30%, 70.59%, and 29.42% for the category, target, and regression tasks, respectively. The 80.22% correlation coefficient of the Afro-XLMR-large model indicates strong alignments.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.