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Model selection/optimization in conformal inference is challenging, since it may break the exchangeability between labeled and unlabeled data. We study this problem in the context of conformal selection, which uses conformal p-values to select ``interesting'' instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. For validity, existing solutions require the model choice to be independent of the data used to construct the p-values and calibrate the selection set. However, when presented with many model choices and limited labeled data, it is desirable to (i) select the best model in a data-driven manner, and (ii) mitigate power loss due to sample splitting. This paper presents OptCS, a general framework that allows valid statistical testing (selection) after flexible data-driven model optimization. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control via a novel multiple testing procedure. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting the most powerful one among multiple pre-trained candidate models, (ii) using all data for model fitting without sample splitting, and (iii) combining full-sample model fitting and selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and alignment of large language models in radiology report generation.

In the one-dimensional facility assignment problem, m facilities and n agents are positioned along the real line. Each agent will be assigned to a single facility to receive service. Each facility incurs a building cost, which is shared equally among the agents utilizing it. Additionally, each agent independently bears a connection cost to access a facility. Thus, an agent's cost is the sum of the connection cost and her portion of the building cost. The social cost is the total cost of all agents. Notably, the optimal assignment that minimizes the social cost can be found in polynomial time. In this paper, we study the problem from two game-theoretical settings regarding the strategy space of agents and the rule the assignment. In both settings, agents act strategically to minimize their individual costs. In our first setting, the strategy space of agents is the set of facilities, granting agents the freedom to select any facility. Consequently, the self-formed assignment can exhibit instability, as agents may deviate to other facilities. We focus on the computation of an equilibrium assignment, where no agent has an incentive to unilaterally change her choice. We show that we can compute a pure Nash equilibrium in polynomial time. In our second setting, agents report their positions to a mechanism for assignment to facilities. The strategy space of agents becomes the set of all positions. Our interest lies in strategyproof mechanisms. It is essential to note that the preference induced by the agents' cost function is more complex as it depends on how other agents are assigned. We establish a strong lower bound against all strategyproof and anonymous mechanisms: none can achieve a bounded social cost approximation ratio. Nonetheless, we identify a class of non-trivial strategyproof mechanisms for any n and m that is unanimous and anonymous.

This paper presents a novel probabilistic detection scheme called Cooperative Statistical Detection~(CSD) for abnormal node detection while defending against adversarial attacks in cluster-tree wireless sensor networks. The CSD performs a two-phase process: 1) designing a likelihood ratio test~(LRT) for a non-root node at its children from the perspective of packet loss; 2) making an overall decision at the root node based on the aggregated detection data of the nodes over tree branches. In most adversarial scenarios, malicious children knowing the detection policy can generate falsified data to protect the abnormal parent from being detected. To resolve this issue, a mechanism is presented in the CSD to remove untrustworthy information. Through theoretical analysis, we show that the LRT-based method achieves the perfect detection. Furthermore, the optimal removal threshold is derived for falsifications with uncertain strategies and guarantees perfect detection of the CSD. As our simulation results shown, the CSD approach is robust to falsifications and can rapidly reach $99\%$ detection accuracy, even in existing adversarial scenarios, which outperforms the state-of-the-art technology., Comment: 12 pages, 12 figures

The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set problem and Multiway Cut problem. SFVS remains NP-hard even in split and chordal graphs, and SFVS in Chordal Graphs (SFVS-C) can be considered as an implicit 3-Hitting Set problem. However, it is not easy to solve SFVS-C faster than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica 2019) proved that SFVS-C can be solved in $\mathcal{O}^{*}(2^{k})$ time, slightly improving the best result $\mathcal{O}^{*}(2.076^{k})$ for 3-Hitting Set. In this paper, we break the "$2^{k}$-barrier" for SFVS-C by giving an $\mathcal{O}^{*}(1.820^{k})$-time algorithm. Our algorithm uses reduction and branching rules based on the Dulmage-Mendelsohn decomposition and a divide-and-conquer method., Comment: 33 pages, 9 figures. Full version

The facility location game has been studied extensively in mechanism design. In the classical model, each agent's cost is solely determined by her distance to the nearest facility. In this paper, we introduce a novel model where each facility charges an entrance fee. Thus, the cost of each agent is determined by both the distance to the facility and the entrance fee of the facility. In our model, the entrance fee function is allowed to be an arbitrary function, causing agents' preferences may no longer be single-peaked anymore: This departure from the classical model introduces additional challenges. We systematically delve into the intricacies of the model, designing strategyproof mechanisms with favorable approximation ratios. Additionally, we complement these ratios with nearly-tight impossibility results. Specifically, for one-facility and two-facility games, we provide upper and lower bounds for the approximation ratios given by deterministic and randomized mechanisms with respect to utilitarian and egalitarian objectives., Comment: A preliminary version of this article appeared at AAAI '23

By means of the nuclear parton distributions determined without the fixed-target Drell-Yan experimental data and the analytic expression of quenching weight based on BDMPS formalism, a next-to-leading order analyses are performed on the Drell-Yan differential cross section ratios from Fermilab E906 and E866 Collaborations. It is found that the calculated results with only the nuclear effects of parton distribution are not in agreement with the E866 and E906 experimental data. The incoming parton energy loss effect can not be ignored in the nuclear Drell-Yan reactions. The predicted results indicate that with the quark transport coefficient as a constant, the suppression due to the target nuclear geometry effect is approximately 19.24% for the quark transport coefficient. It is shown that we should consider the target nuclear geometry effect in studying the Drell-Yan reaction on nuclear targets. On the basis of Bjorken variable and scale dependence of the quark transport coefficient, the atomic mass dependence is incorporated. The quark transport coefficient is determined as a function of the atomic mass, Bjorken variable $x_2$ and scale $Q^2$ by the global fit of the experimental data. The determined constant factor $\hat{q}_0$ of the quark transport coefficient is $0.061\pm0.004 {\rm GeV^2/fm}$. It is found that the atomic mass dependence has a remarkable impact on the constant factor $\hat{q}_0$ in the quark transport coefficient in cold nuclear matter., Comment: arXiv admin note: text overlap with arXiv:2012.03167

Gravitational wave signal from the inspiral of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspiral covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly $30\%$ through detections of $10$ gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of $< 10 \%$, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within $5\%$ precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about $1\%$. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P$-$P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant., Comment: 29 pages, 14 figures, update to match published version

The Drell-Yan process for proton incident on nuclei is an excellent place for deeply studying the parton propagation in a nucleus. By means of the nuclear parton distributions determined only with lepton-nuclear deep inelastic scattering experimental data and the analytic parameterization of quenching weight based on BDMPS formalism, a phenomenological analysis of the nuclear Drell-Yan differential cross section ratio as a function of Feynman variable is performed from Fermilab E906 and E866 experimental data. With the nuclear geometry effect on nuclear Drell-Yan process and the quark transport coefficient as a constant, our predictions are in good agreement with the experimental measurements. It is found that nuclear geometry effect has a significant impact on the quark transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the nuclear Drell-Yan process. Our calculated results reveal that the difference in the values of quark transport coefficient exists from E906 and E866 experiments. However, confirming the conclusion that the quark transport coefficient depends on the target-quark momentum fraction, still need more accurate experimental data on the Drell-Yan differential cross section ratio in the future. Three models are proposed and discussed for the quark transport coefficient as a function of the measurable kinematic variables. The quark transport coefficient $\hat{q}$ is determined as a function of the Bjorken variable $x_2$ and scale $Q^2$. It is hoped that the parametrization form of quark transport coefficient in the cold nuclear medium can help to think about the parton propagation mechanism in nuclear matter., Comment: arXiv admin note: text overlap with arXiv:2011.14350

Nuclear modification of hadron production in deep inelastic lepton-nucleus scattering can be applied to study the parton propagation mechanism in cold nuclear matter. By means of the analytic parameterization of quenching weight based on BDMPS formalism with the target nuclear geometry effect, the leading-order computations for hadron multiplicity ratios are performed with comparison to the HERMES charged pions production data on the quarks hadronization occurring outside the nucleus. The relation is discovered between quark transport coefficient and the measurable kinematic variables in deep inelastic scattering. Four models are proposed on the quark transport coefficient. The constant model, the power-law model and the double power-law model can be ruled out because of the experimental fact that the transverse momentum broadening increases as a function of the photon virtuality $Q^2$. The quark transport coefficient is determined as a function of the Bjorken variable $x$ and scale $Q^2$. The trend of quark transport coefficient in respect of Bjorken variable $x$ and scale $Q^2$ is qualitatively in partial agreement with HERMES experimental data on transverse momentum broadening. It is hoped that our effort is conducive to understanding of jet quenching phenomenon in relativistic heavy ion collisions.