Motivated by the success of general‑purpose large language models (LLMs) in software patching, recent works started to train specialized patching models. Most works trained one model to handle the end‑to‑end patching pipeline (including issue localization, patch generation, and patch validation). However, it is hard for a small model to handle all tasks, as different sub-tasks have different workflows and require different expertise. As such, by using a 70 billion model, SOTA methods can only reach up to 41% resolved rate on SWE-bench-Verified. Motivated by the collaborative nature, we propose Co-PatcheR, the first collaborative patching system with small and specialized reasoning models for individual components. Our key technique novelties are the specific task designs and training recipes. First, we train a model for localization and patch generation. Our localization pinpoints the suspicious lines through a two-step procedure, and our generation combines patch generation and critique. We then propose a hybrid patch validation that includes two models for crafting issue-reproducing test cases with and without assertions and judging patch correctness, followed by a majority vote-based patch selection. Through extensive evaluation, we show that Co-PatcheR achieves 46% resolved rate on SWE-bench-Verified with only 3 x 14B models. This makes Co-PatcheR the best patcher with specialized models, requiring the least training resources and the smallest models. We conduct a comprehensive ablation study to validate our recipes, as well as our choice of training data number, model size, and testing-phase scaling strategy.

Our paper proposes a direct sparse visual odometry method that combines event and RGBD data to estimate the pose of agile-legged robots during dynamic locomotion and acrobatic behaviors. Event cameras offer high temporal resolution and dynamic range, which can eliminate the issue of blurred RGB images during fast movements. This unique strength holds a potential for accurate pose estimation of agile- legged robots, which has been a challenging problem to tackle. Our framework leverages the benefits of both RGBD and event cameras to achieve robust and accurate pose estimation, even during dynamic maneuvers such as jumping and landing a quadruped robot, the Mini-Cheetah. Our major contributions are threefold: Firstly, we introduce an adaptive time surface (ATS) method that addresses the whiteout and blackout issue in conventional time surfaces by formulating pixel-wise decay rates based on scene complexity and motion speed. Secondly, we develop an effective pixel selection method that directly samples from event data and applies sample filtering through ATS, enabling us to pick pixels on distinct features. Lastly, we propose a nonlinear pose optimization formula that simultaneously performs 3D-2D alignment on both RGB-based and event-based maps and images, allowing the algorithm to fully exploit the benefits of both data streams. We extensively evaluate the performance of our framework on both the public dataset and our own quadruped robot dataset, demonstrating its effectiveness in accurately estimating the pose of agile robots during dynamic movements. Supplemental video: https://youtu.be/-5ieQShOg3M

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for Rayleigh fading channels, instead of implementing the complex design procedures targeted, specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also show that eIRA codes designed for the BuEC enjoy the advantage of efficient encodability and a lower error-rate floor. Finally, we demonstrate that it is the distribution of the number of faded bits per codeword which determines the difference between correlated and uncorrelated fading channel performance. Perfect channel state information is assumed in this paper.

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes (a class of efficiently encodable LDPC codes) for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for the Rayleigh fading channel, instead of implementing the complex design procedures targeted specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also derive a new channel statistic, the distribution of the number of faded bits per codeword which determines the difference between the performance of correlated and uncorrelated (ideally interleaved) fading channels.

Full-text indexing of documents containing mathematics cannot be considered a complete success unless the mathematics symbolism is extracted and represented in a standardized form permitting both searching for formulas, and re-use of this information in (for example) computer algebra systems. Most documents produced in the past and subsequently digitally encoded, and even most of those potentially "born digital" in current journal production are---at best---encoded in a printer form such as Adobe Postscript [1], in which mathematics is not explicitly marked or easily identifiable. While one might look forward in the future to other document encodings such as MathML, the common journal or textbook product is essentially without semantic content: a jumble of odd characters. Sometimes it is just a jumble of black and white dots! In this paper we demonstrate an approach to decoding, to recognizing and extracting mathematical expressions, from a Postscript document. We can produce a syntactic representation of the extracted expressions which can then be used to generate various forms. For example, if we extract TeX or Presentation MathML, we can re-typeset the expression, but perhaps in a different size or font family. More significantly, if we start from this presentation information, we can hope to combine it with additional contextual processing of the surrounding text and meta-data associated with the document, to assign semantics,(e.g. content MathML), or provide versions in computer algebra system languages such as Maple or Mathematica. Finally, it is possible to use this material to present audio or braille versions of mathematics for the visually disabled. We have previously addressed some aspects of the higher level of processing (parsing TeX for example). In this paper we address the only first stage and concentrate on what may seem to be overly simple, but is in fact difficult to do precisely: extracting the mathematics parts from text.

This paper presents a new class of irregular low-density parity-check (LDPC) codes of moderate length (10/sup 3//spl les/n/spl les/10/sup 4/) and high rate (R/spl ges/3/4). Codes in this class admit low-complexity encoding and have lower error-rate floors than other irregular LDPC code-design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit-error rate of 10/sup -9/ are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates.

We consider in this paper the possibility of a cyclic or quasi-cyclic LDPC code as the complete error control system in a magnetic recording channel. Thus, we compare the performance of selected LDPC codes with two Reed-Solomon (RS) code schemes on an EPR4 channel, with particular emphasis on their performance in noise bursts (induced by thermal asperities). We find some very promising initial results in that the LDPC codes are very robust against large noise burst (128 bits long), and are superior to the RS schemes examined in the measurable error rate region. The extent to which they are superior depends on the particular LDPC scheme involved, and the results provide motivation for further investigation in this area.