arXiv subjects

Dmitri Shmelkin

Publications and source records attributed to Dmitri Shmelkin.

5 recordsLinked to original sources

arXiv2026

Algorithm to check Maximum Likelihood Estimate Existence for integrated PCA

Being encouraged by [AKRS] that provides an amazing bridge between Statistics and Invariant Theory, and especially by [FM], where quiver semi-invariant techniques apply to verify the existence of MLE for a recent iPCA model, we provide an enhancement to [FM]. Our Theorem 5.2 yields necessary and sufficient conditions for MLE to exist generically for any dimension vector. The conditions can be easily checked with either of our software [T] or [FF] based on Derksen-Weyman algorithm. This simplifies the application for statistics practitioners and non-specialists in quivers. For those deep in quiver Representation Theory, Theorem 5.2 relates the MLE existence to the local semi-simplicity of representations as introduced in [Sh07]. Moreover, we implemented in [FF] the Flip-Flop algorithm from [TA] and checked that it does work in all cases guaranteed by Theorem 5.2. We hope that our elementary and short text can serve for the experts in both domains as a warm start in a new category. And we welcome practitioners to use our code at [FF] for their own experiments.

math.ST↗

arXiv2026

Pipeline for Verifying LLM-Generated Mathematical Solutions

With the growing popularity of Large Reasoning Models and their results in solving mathematical problems, it becomes crucial to measure their capabilities. We introduce a pipeline for both automatic and interactive verification as a more accurate alternative to only checking the answer which is currently the most popular approach for benchmarks. The pipeline can also be used as a generator of correct solutions both in formal and informal languages. 3 AI agents, which can be chosen for the benchmark accordingly, are included in the structure. The key idea is the use of prompts to obtain the solution in the specific form which allows for easier verification using proof assistants and possible use of small models ($\le 8B$). Experiments on several datasets suggest low probability of False Positives. The open-source implementation with instructions on setting up a server is available at https://github.com/LogicEnj/lean4_verification_pipeline.

cs.AI↗

arXiv2024

Efficient Mixed Integer Linear Programming Approaches to Dynamic Path Restoration

We consider the problem of single link failure in an elastic optical network, (also known as flex-grid WDM network). The task is to reroute optical connections that go through the broken link using free capacity of other links of the network. Nowadays, dynamic restoration gains popularity, in which the possiblity of rerouting is only inspected after a link failure is detected. Since the problem of recovery is NP-hard, heuristic algorithms are used to either find such routes, or suggest that the routes do not exist. In order to understand the quality of these heuristics, often mixed integer linear programming is used to obtain exact positive and negative answers. We present a detailed such model that checks whether restoration is possible without the use of additional regenerators. This means, that the new light paths need to satisfy a length constraint. As preprossing we apply a trimming procedure that takes advantage of this length constraint, and significantly speeds up the evaluation of these models. Our model is more general, and besides solving the problem of link restoration, also solves the full problem of wavelength and spectrum assignment.

cs.NI↗

arXiv2019

Conservative Link Adaptation for Ultra Reliable Low Latency Communications

Ultra reliable low latency communications (URLLC) is one of the most promising and demanding services in 5G systems. This service requires very low latency of less than $1-10$ ms and very high transmission reliability: the acceptable packet loss ratio is about $10^{-5}$. To satisfy such strict requirements, many issues shall be solved. This paper focuses on the link adaptation problem, i.e., the selection of a modulation and coding scheme (MCS) for transmission based on the received channel quality indicator (CQI) reports. On the one hand, link adaptation should select a robust MCS to provide high reliability. On the other hand, it should select the highest possible MCS to reduce channel resource consumption. The paper shows that even for one URLLC user, link adaptation is still a challenging problem, especially in highly-variant channels. To solve this problem, a conservative link adaptation algorithm is designed. The algorithm estimates the strongest channel degradation at the time moment of the actual packet transmission and selects an MCS taking into account the worst degradation. The obtained results show that the proposed algorithm is efficient in terms of both the packet loss ratio and the channel resource consumption.

cs.NI↗

arXiv2018

Lookup Lateration: Mapping of Received Signal Strength to Position for Geo-Localization in Outdoor Urban Areas

The accurate geo-localization of mobile devices based upon received signal strength (RSS) in an urban area is hindered by obstacles in the signal propagation path. Current localization methods have their own advantages and drawbacks. Triangular lateration (TL) is fast and scalable but employs a monotone RSS-to-distance transformation that unfortunately assumes mobile devices are on the line of sight. Radio frequency fingerprinting (RFP) methods employ a reference database, which ensures accurate localization but unfortunately hinders scalability. Here, we propose a new, simple, and robust method called lookup lateration (LL), which incorporates the advantages of TL and RFP without their drawbacks. Like RFP, LL employs a dataset of reference locations but stores them in separate lookup tables with respect to RSS and antenna towers. A query observation is localized by identifying common locations in only associating lookup tables. Due to this decentralization, LL is two orders of magnitude faster than RFP, making it particularly scalable for large cities. Moreover, we show that analytically and experimentally, LL achieves higher localization accuracy than RFP as well. For instance, using grid size 20 m, LL achieves 9.11 m and 55.66 m, while RFP achieves 72.50 m and 242.19 m localization errors at 67\% and 95\%, respectively, on the Urban Hannover Scenario dataset.

cs.NI↗