Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this challenge, we propose CAusal MAthematician (CAMA), a two stage causal framework that equips LLMs with explicit, reusable mathematical structure. In the learning stage, CAMA first constructs the Mathematical Causal Graph (MCG), a high level representation of solution strategies, by combining LLM priors with causal discovery algorithms applied to a corpus of question solution pairs. The resulting MCG encodes essential knowledge points and their causal dependencies. To better align the graph with downstream reasoning tasks, CAMA further refines the MCG through iterative feedback derived from a selected subset of the question solution pairs. In the reasoning stage, given a new question, CAMA dynamically extracts a task relevant subgraph from the MCG, conditioned on both the question content and the LLM’s intermediate reasoning trace. This subgraph, which encodes the most pertinent knowledge points and their causal dependencies, is then injected back into the LLM to guide its reasoning process. Empirical results on real world datasets show that CAMA significantly improves LLM performance on challenging mathematical problems. Furthermore, our experiments demonstrate that structured guidance consistently outperforms unstructured alternatives, and that incorporating asymmetric causal relationships yields greater improvements than using symmetric associations alone.

This paper explores three key aspects of causal discovery from heterogeneous time series. First, it introduces a method that uses (conditional) mutual information to determine (conditional) independence among diverse qualitative and quantitative variables, alongside a novel local permutation test. Next, the paper presents a new algorithm for identifying event-based causal relations in threshold-based IT systems for root cause analysis. This method is effective when root causes are not causally related, and an extension involving agent intervention is proposed to address this limitation. Both the algorithm and its extension utilize causal discovery from offline data and subgraph traversal for new anomalies in online data. Finally, the paper addresses time series with multiple piecewise consistent regimes, each having distinct causal mechanisms. The proposed method segments the time series into appropriate regimes and identifies the correct window causal graph, capturing both instantaneous and lagged connections within each regime. Experiments with synthetic data confirm the effectiveness of the proposed methods.

This paper introduces a new structural causal model tailored for representing threshold-based IT systems and presents a new algorithm designed to rapidly detect root causes of anomalies in such systems. When root causes are not causally related, the method is proven to be correct; while an extension is proposed based on the intervention of an agent to relax this assumption. Our algorithm and its agent-based extension leverage causal discovery from offline data and engage in subgraph traversal when encountering new anomalies in online data. Our extensive experiments demonstrate the superior performance of our methods, even when applied to data generated from alternative structural causal models or real IT monitoring data.

This paper presents an approach for identifying the root causes of collective anomalies given observational time series and an acyclic summary causal graph which depicts an abstraction of causal relations present in a dynamic system at its normal regime. The paper first shows how the problem of root cause identification can be divided into many independent subproblems by grouping related anomalies using d-separation. Further, it shows how, under this setting, some root causes can be found directly from the graph and from the time of appearance of anomalies. Finally, it shows, how the rest of the root causes can be found by comparing direct effects in the normal and in the anomalous regime. To this end, an adjustment set for identifying direct effects is introduced. Extensive experiments conducted on both simulated and real-world datasets demonstrate the effectiveness of the proposed method.

In mobile wireless systems, the quest to support delay-stringent multimedia applications challenges most existing solutions to the mobility support and traffic management problems. An infrastructure supported approach is required to provide non-disrupted services with seamless roaming capabilities. We propose a mobility management scheme called personal AP, to support station mobility efficiently. In personal AP mobility support system, the mobility context of each mobile station is defined by the relevant state information at the currently associated access point, including the MAC layer association states at the access point. When the mobile station roams, the access point context follows the mobile station from one physical access point to another, thus creating the "ghost" access point following the mobile station and eliminating the mobile station from re-associating with new access points. Personal AP system improve the seamless roaming support by avoid the lengthy re-association process commonly seen in IEEE 802.11 systems. The essential idea of personal AP is applicable in other wireless systems as well.

Opportunistic beamforming with proportional fair scheduling is a very promising technique that exploits multiuser diversity to achieve high data rates on the downlink while ensuring a certain level of fairness. However, it greatly improves system performance only for a sufficiently large mobile user population. This paper proposes a technique enhancing opportunistic beamforming at the transmitter with antenna selection at each mobile receiver to overcome this limitation. Significant performance improvement is achieved, especially for small number of users. The simplicity and inexpensive deployment of this technique make it a highly desirable enhancement to opportunistic beamforming.

The demands for multimedia and packet data services over wireless devices have increased over the past few years. The direct impact on performance makes scheduling for real-time traffic important. This paper presents a novel scheduling algorithm called fair channel-dependent scheduling which schedules packet delivery to mobile stations in a fair manner and at the same time takes into consideration the channel conditions for power efficiency. With added delay information for real-time traffic, this approach aims at delivering real-time traffic in a timely manner, while maintaining a balance between power conservation and fairness. Through comparative simulations with two conventional scheduling algorithms, we show that our scheme indeed achieves better overall performance than comparable scheduling schemes.