On Discrete Truthful Heterogeneous Two-Facility Location

We revisit the discrete heterogeneous two-facility location problem, in which there is a set of agents that occupy nodes of a line graph, and have private approval preferences over two facilities. When the facilities are located at some nodes of the line, each agent derives a cost that is equal to her total dis- tance from the facilities she approves. The goal is to decide where to locate the two facilities, so as to (a) incentivize the agents to truthfully report their preferences, and (b) achieve a good approximation of the minimum total (social) cost or the maximum cost among all agents. For both objectives, we de- sign deterministic strategyproof mechanisms with approximation ratios that significantly outperform the state-of-the-art, and complement these results with (almost) tight lower bounds

The Distortion of Distributed Facility Location

We study the distributed facility location problem, where a set of agents with positions on the line of real numbers are partitioned into disjoint districts, and the goal is to choose a point to satisfy certain criteria, such as optimize an objective function or avoid strategic behavior. A mechanism in our distributed setting works in two steps: For each district it chooses a point that is representative of the positions reported by the agents in the district, and then decides one of these representative points as the final output. We consider two classes of mechanisms: Unrestricted mechanisms which assume that the agents directly provide their true positions as input, and strategyproof mechanisms which deal with strategic agents and aim to incentivize them to truthfully report their positions. For both classes, we show tight bounds on the best possible approximation in terms of several minimization social objectives, including the well-known average social cost (average total distance of agents from the chosen point) and max cost (maximum distance among all agents from the chosen point), as well as other fairness-inspired objectives that are tailor-made for the distributed setting, in particular, the max-of-average and the average-of-max

Mechanism Design without Money for Heterogeneous and Distributed Facility Location Problems

Algorithmic Mechanism Design (AMD) is an interdisciplinary field that bridges economics and computer science and aims to design mechanisms for systems with self-interested agents. This study focuses on motivating truthful information disclosure while optimizing social goals. Traditional payment-based mechanisms cannot be effectively applied to some of these problems, but we can utilize approximate mechanisms to obtain truthfulness without recourse to payments. One of the well-established problems in approximate mechanism design without money is the facility location problem. In this context, agents possess private positions along a line, and the goal is to determine the location of a public facility while motivating truthful disclosures and achieving optimal social outcomes. This thesis presents contributions across three key dimensions of facility location problems: (1) Heterogeneous Two-Facility Location Problem: Addressing a discrete setting where agents occupy nodes on a line graph and possess private preferences for two facilities, the research introduces deterministic strategy-proof mechanisms with improved approximation ratios, surpassing existing approaches. (2) Two-Facility Location with Candidate Positions: Investigating another variant, where agents have private positions and known preferences for two facilities, the study identifies deterministic strategy-proof mechanisms that achieve the best possible approximation ratios for social and maximum costs. (3) Distributed Facility Location Problem: A set of agents with positions on the line of real numbers are partitioned into disjoint districts, we designed deterministic distributed mechanisms that satisfy various criteria of interest and achieve the best possible distortion bounds. The research analyzes two mechanism classes: Unrestricted, where agents directly provide truthful positions, and strategy-proof, designed to incentivize honesty. The study establishes tight bounds for various social objectives, including average social cost, max cost, and other fairness-inspired criteria. In summary, approximate mechanism design without money addresses complex challenges in multi-agent systems, creating mechanisms that promote truthfulness and optimize societal objectives. This thesis introduces innovative mechanisms and provides comprehensive insights into facility location problems from three distinct perspectives

Mechanical Properties and Energy Damage Evolution Mechanism of Basalt Fiber-Modified Tailing Sand Cementation and Filling Body Mechanics

In order to investigate the mechanical properties of basalt fiber-doped tailing sand cemented filler and the evolution of energy damage, a uniaxial compression test was carried out on the basalt fiber-doped tailing sand cemented filler specimens to analyze the energy dissipation characteristics, and the damage constitutive equations with different basalt fiber contents were established based on damage mechanics. The results show that with the increase of fiber doping and fiber length, the uniaxial compressive strength and ductility of the filling body show a trend of increasing and then decreasing; the optimal value of fiber doping is 0.6%, and the optimal value of fiber length is 9 mm; the total strain energy, elastic strain energy and dissipation energy of basalt fiber-modified tailing sand cemented filling body at peak stress show a trend of increasing and then decreasing, and the energy dissipation energy of the filling body shows a trend of increasing and then decreasing. The energy dissipation energy shows a trend of increasing and then decreasing, and the energy dissipation energy shows a trend of increasing and then decreasing. The total strain energy, elastic strain energy, and dissipation energy at the peak stress show a trend of decreasing after increasing with the fiber doping and fiber length, and the energy damage evolution process can be divided into four stages: no damage stage, stable damage development stage, accelerated damage growth stage, and damage destruction; in addition, the existing damage constitutive model of the fiber-filled body was optimized, and the damage correction factor was introduced to obtain the damage constitutive model of the filled body with different fiber contents, and finally, after the verification of experimental and theoretical models, it was found that the two stress–strain curves coincided well. Finally, after the test and theoretical model verification, it is found that the stress–strain curves of the two are in good agreement, which indicates that the established theoretical model has a certain reference value for engineering practice, and at the same time, it has certain limitations

Lactobacillus reuteri mitigates hepatic ischemia/reperfusion injury by modulating gut microbiota and metabolism through the Nrf2/HO-1 signaling

Abstract Background This study seeks to investigate the impacts of Lactobacillus reuteri (L. reuteri) on hepatic ischemia-reperfusion (I/R) injury and uncover the mechanisms involved. Methods Mice in the I/R groups were orally administered low and high doses of L.reuteri (L.reuteri-low and L. reuteri-hi; 1 × 1010 CFU/d and 1 × 1011 CFU/d), for 4 weeks prior to surgery. Following this, mice in the model group were treated with an Nrf2 inhibitor (ML-385), palmitoylcarnitine, or a combination of both. Results After treatment with L. reuteri, mice exhibited reduced levels of serum aminotransferase (ALT), aspartate aminotransferase (AST), and myeloperoxidase (MPO) activity, as well as a lower Suzuki score and apoptosis rate. L. reuteri effectively reversed the I/R-induced decrease in Bcl2 expression, and the significant increases in the levels of Bax, cleaved-Caspase3, p-p65/p65, p-IκB/IκB, p-p38/p38, p-JNK/JNK, and p-ERK/ERK. Furthermore, the administration of L. reuteri markedly reduced the inflammatory response and oxidative stress triggered by I/R. This treatment also facilitated the activation of the Nrf2/HO-1 pathway. L. reuteri effectively counteracted the decrease in levels of beneficial gut microbiota species (such as Blautia, Lachnospiraceae NK4A136, and Muribaculum) and metabolites (including palmitoylcarnitine) induced by I/R. Likewise, the introduction of exogenous palmitoylcarnitine demonstrated a beneficial impact in mitigating hepatic injury induced by I/R. However, when ML-385 was administered prior to palmitoylcarnitine treatment, the previously observed effects were reversed. Conclusion L. reuteri exerts protective effects against I/R-induced hepatic injury, and its mechanism may be related to the promotion of probiotic enrichment, differential metabolite homeostasis, and the Nrf2/HO-1 pathway, laying the foundation for future clinical applications

Energy Management System Architecture for New Energy Power Supply System of Islands

8 Halama