Search

We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems differ in the objective function, which determines which partition is the best one. These problems have applications in community detection, cybersecurity, and bioinformatics. We present integer non-linear formulations, which are then linearized using standard techniques. To solve these formulations, we develop exact branch-and-cut algorithms, embedding various improving techniques, such as valid inequalities, bounds limiting the number of variables, and warm-start and preprocessing techniques. Extensive computational tests on benchmark instances demonstrate the effectiveness of the proposed procedures. The branch-and-cut algorithms can solve reasonably sized instances efficiently. To the best of our knowledge, we are the first to propose an exact algorithm for solving these problems.

A long-term measurement was conducted to search for $\alpha$, double-$\alpha$ and double-$\beta$ decays with $\gamma$ quanta emission in naturally occurring osmium isotopes. This study took advantage of two ultra-low background HPGe detectors and one ultra-low background BEGe detector at the Gran Sasso National Laboratory (LNGS) of the INFN. Over almost 5 years of data were taken using high-purity osmium samples of approximately 173 g. The half-life limits set for a decays of $^{184}$Os to the first $2^+$ 103.6 keV excited level of $^{180}$W ($T_{1/2} > 9.3 \times 10^{15}$ yr) and of $^{186}$Os to the first $2^+$ 100.1 keV of $^{182}$W ($T_{1/2} > 4.8 \times 10^{17}$ yr) exceed substantially the present theoretical predictions that are at level of $T_{1/2} \sim (0.6 - 3) \times 10^{15}$ yr for $^{184}$Os and $T_{1/2} \sim (0.3 - 2) \times 10^{17}$ yr for $^{186}$Os. New half-life limits on the 2EC and EC$\beta^+$ decay of $^{184}$Os to the ground and excited levels of $^{184}$W were set at level of $T_{1/2} > 10^{16} - 10^{17}$ yr; a lower limit on the $2\beta^-$ decay of $^{192}$Os to the $2^+$ 316.5 keV excited level of $^{192}$Pt was estimated as $T_{1/2} > 6.1 \times 10^{20}$ yr. The half-life limits for $2\alpha$ decay of $^{189}$Os and $^{192}$Os were set for the first time at level of $T_{1/2} > 10^{20}$ yr., Comment: 38 pages, 17 figures, 5 tables

Aircraft conflict resolution is one of the major tasks of computer-aided air traffic management and represents a challenging optimization problem. Many models and methods have been proposed to assist trajectory regulation to avoid conflicts. However, the question of testing the different mathematical optimization approaches against each other is still open. Standard benchmarks include unrealistic scenarios in which all the flights move toward a common point or completely random generated instances. There is a lack of a common set of test instances that allows comparison of the available methods under a variety of heterogeneous and representative scenarios. We present a flight deconfliction benchmark generator that allows the user to choose between (i) different predefined scenario inspired by existing benchmarks in the literature; (ii) pseudo-random traffic meeting certain congestion measurements; (iii) and randomly generated traffic. The proposed setting can account for different levels of difficulty in the deconfliction of the aircraft and allows to explore and compare the real limitations of optimization approaches for aircraft conflict resolution.

We conceptualize in the paper the linear degenerate symplectic flag varieties as symmetric degenerations within the framework of type $A$ equioriented quivers. First, in the larger context of symmetric degenerations, we give a self-contained proof of the equivalence of different degeneration orders. Furthermore, we investigate the PBW locus: geometric properties of the degenerate varieties in this locus are proved by realizing them from different perspectives., Comment: 23 pages

This paper deals with optimal policy learning (OPL) with observational data, i.e. data-driven optimal decision-making, in multi-action (or multi-arm) settings, where a finite set of decision options is available. It is organized in three parts, where I discuss respectively: estimation, risk preference, and potential failures. The first part provides a brief review of the key approaches to estimating the reward (or value) function and optimal policy within this context of analysis. Here, I delineate the identification assumptions and statistical properties related to offline optimal policy learning estimators. In the second part, I delve into the analysis of decision risk. This analysis reveals that the optimal choice can be influenced by the decision maker's attitude towards risks, specifically in terms of the trade-off between reward conditional mean and conditional variance. Here, I present an application of the proposed model to real data, illustrating that the average regret of a policy with multi-valued treatment is contingent on the decision-maker's attitude towards risk. The third part of the paper discusses the limitations of optimal data-driven decision-making by highlighting conditions under which decision-making can falter. This aspect is linked to the failure of the two fundamental assumptions essential for identifying the optimal choice: (i) overlapping, and (ii) unconfoundedness. Some conclusions end the paper.

The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this problem using a tailored Kernel Search heuristic method, which consists in solving iteratively improved restrictions of the problem. The main novelty of the approach consists in using an independent set of the conflict graph within the algorithm. We test our approach on the benchmark instances and we compare our results with the ones obtained by other heuristics available in the literature.

Rare-event search experiments located on-surface, such as short-baseline reactor neutrino experiments, are often limited by muon-induced background events. Highly efficient muon vetos are essential to reduce the detector background and to reach the sensitivity goals. We demonstrate the feasibility of deploying organic plastic scintillators at sub-Kelvin temperatures. For the NUCLEUS experiment, we developed a cryogenic muon veto equipped with wavelength shifting fibers and a silicon photo multiplier operating inside a dilution refrigerator. The achievable compactness of cryostat-internal integration is a key factor in keeping the muon rate to a minimum while maximizing coverage. The thermal and light output properties of a plastic scintillation detector were examined. We report first data on the thermal conductivity and heat capacity of the polystyrene-based scintillator UPS-923A over a wide range of temperatures extending below one Kelvin. The light output was measured down to 0.8K and observed to increase by a factor of 1.61$\pm$0.05 compared to 300K. The development of an organic plastic scintillation muon veto operating in sub-Kelvin temperature environments opens new perspectives for rare-event searches with cryogenic detectors at sites lacking substantial overburden.

Solving convex Semi-Infinite Programming (SIP) problems is challenging when the separation problem, i.e., the problem of finding the most violated constraint, is computationally hard. We propose to tackle this difficulty by solving the separation problem approximately, i.e., by using an inexact oracle. Our focus lies in two algorithms for SIP, namely the Cutting-Planes (CP) and the Inner-Outer Approximation (IOA) algorithms. We prove the CP convergence rate to be in O(1/k), where k is the number of calls to the limited-accuracy oracle, if the objective function is strongly convex. Compared to the CP algorithm, the advantage of the IOA algorithm is the feasibility of its iterates. In the case of a semi-infinite program with Quadratically Constrained Quadratic Programming separation problem, we prove the convergence of the IOA algorithm toward an optimal solution of the SIP problem despite the oracle's inexactness.

The emission of $\gamma$-rays after a neutron capture in a cryogenic detector can generate mono-energetic nuclear recoils in the sub-keV regime, of direct interest for the calibration of Dark Matter and Coherent Elastic Neutrino Nucleus Scattering experiments. Here we show that accurate predictions of the nuclear recoil spectra induced by neutron captures require taking into account the interplay between the development in time of the de-excitation $\gamma$-cascade of the target nucleus and that of the associated atomic collisions in matter. We present detailed simulations coupling the FIFRELIN code for the description of the $\gamma$-cascades and the IRADINA code for the modelling of the fast atomic movements in matter. Nuclear recoil spectra are predicted, and made available to the community, for concrete cases of Al$_2$O$_3$, Si, Ge and CaWO$_4$ crystals exposed to a low intensity beam of thermal neutrons. We find that timing effects cause new calibration peaks to emerge in the recoil spectra and also impact the shape of the continuous recoil distribution. We discuss how they could give access to a rich physics program, spanning the accurate study of the response of cryogenic detectors in the sub-keV range, tests of solid state physics simulations and tests of nuclear models.

In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. Since the carriers are not under the platform's control, the platform has to anticipate their reactions, while deciding how to allocate the delivery operations. Indeed, carriers' decisions largely affect the platform's revenue. In this paper, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. Possibly, the platform can influence carriers' decisions by determining also the compensation paid for each accepted request. The two considered settings result in two different formulations: the bilevel profitable tour problem with fixed compensation margins and with margin decisions, respectively. For each of them, we propose single-level reformulations and alternative formulations where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models, with a tailored warm-start heuristic used to speed up the solution process. Extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics.

Proceedings for our meeting ``What comes beyond the Standard Models'', which covered a broad series of subjects., Comment: This is the proceedings for the 25th Workshop in Bled for "What comes beyond the Standard Models'' including also a webinar "meeting'' using Cosmovia on the same subject

In social network analysis, the size of the k-core, i.e., the maximal induced subgraph of the network with minimum degree at least k, is frequently adopted as a typical metric to evaluate the cohesiveness of a community. We address the Collapsed k-Core Problem, which seeks to find a subset of $b$ users, namely the most critical users of the network, the removal of which results in the smallest possible k-core. For the first time, both the problem of finding the k-core of a network and the Collapsed k-Core Problem are formulated using mathematical programming. On the one hand, we model the Collapsed k-Core Problem as a natural deletion-round-indexed Integer Linear formulation. On the other hand, we provide two bilevel programs for the problem, which differ in the way in which the k-core identification problem is formulated at the lower level. The first bilevel formulation is reformulated as a single-level sparse model, exploiting a Benders-like decomposition approach. To derive the second bilevel model, we provide a linear formulation for finding the k-core and use it to state the lower-level problem. We then dualize the lower level and obtain a compact Mixed-Integer Nonlinear single-level problem reformulation. We additionally derive a combinatorial lower bound on the value of the optimal solution and describe some pre-processing procedures and valid inequalities for the three formulations. The performance of the proposed formulations is compared on a set of benchmarking instances with the existing state-of-the-art solver for mixed-integer bilevel problems proposed in (Fischetti et al., A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs, Operations Research 65(6), 2017)., Comment: Accepted for publication in European Journal of Operational Research; doi: 10.1016/j.ejor.2023.04.038

The NUCLEUS experiment aims to perform a high-precision measurement of Coherent Elastic Neutrino-Nucleus Scattering (CEvNS) at the EdF Chooz B nuclear power plant in France. CEvNS is a unique process to study neutrino properties and to search for physics beyond the Standard Model. The study of CEvNS is also important for light Dark-Matter searches. It could be a possible irreducible background for high-sensitivity Dark-Matter searches. NUCLEUS is an experiment under construction based on ultra-low threshold (20 eVnr) cryogenic calorimeters, operated at tens-of-mK temperatures., Comment: Procceding for 14th International Conference on Identification of Dark Matter Vienna, Austria, 18-22 July 2022 - Submitted to SciPost

Coherent elastic neutrino-nucleus scattering and low-mass Dark Matter detectors rely crucially on the understanding of their response to nuclear recoils. We report the first observation of a nuclear recoil peak at around 112 eV induced by neutron capture. The measurement was performed with a CaWO$_4$ cryogenic detector from the NUCLEUS experiment exposed to a $^{252}$Cf source placed in a compact moderator. The measured spectrum is found in agreement with simulations and the expected peak structure from the single-$\gamma$ de-excitation of $^{183}$W is identified with 3 $\sigma$ significance. This result demonstrates a new method for precise, in-situ, and non-intrusive calibration of low-threshold experiments.

The long-standing model-independent annual modulation effect measured by DAMA deep underground at Gran Sasso Laboratory with different experimental configurations is summarized and perspectives will be highlighted. DAMA/LIBRA-phase2 set-up, $\simeq$ 250 kg highly radio-pure NaI(Tl) confirms the evidence of a signal that meets all the requirements of the model independent Dark Matter annual modulation signature at high C.L.; the full exposure is 2.86 ton $\times$ yr over 22 annual cycles. The experiment is currently collecting data in the DAMA/LIBRA-phase2 empowered configuration with an even lower software energy threshold. Other recent claims are shortly commented., Comment: Proceedings of IDM 2022, July 18-22, 2022. A Section is dedicated to rebut the arguments of arXiv:2208.05158

We define a specialization map between cohomology algebras of quiver Grassmannians of Dynkin type and we prove that it is surjective in type A. This generalizes a result of Lanini and Strickland., Comment: The new version include a new definition of the specialization map for quiver Grassmannians with respect to the one given in the first version. The new definition can be applied to a large class of quiver algebras

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a process in which neutrinos scatter on a nucleus which acts as a single particle. Though the total cross section is large by neutrino standards, CE$\nu$NS has long proven difficult to detect, since the deposited energy into the nucleus is $\sim$ keV. In 2017, the COHERENT collaboration announced the detection of CE$\nu$NS using a stopped-pion source with CsI detectors, followed up the detection of CE$\nu$NS using an Ar target. The detection of CE$\nu$NS has spawned a flurry of activities in high-energy physics, inspiring new constraints on beyond the Standard Model (BSM) physics, and new experimental methods. The CE$\nu$NS process has important implications for not only high-energy physics, but also astrophysics, nuclear physics, and beyond. This whitepaper discusses the scientific importance of CE$\nu$NS, highlighting how present experiments such as COHERENT are informing theory, and also how future experiments will provide a wealth of information across the aforementioned fields of physics., Comment: contribution to Snowmasss 2021. Contact authors: P. S. Barbeau, R. Strauss, L. E. Strigari

Zinc tungstate (ZnWO$_4$) crystal scintillators are promising detection material for the experiments searching for double beta decay, dark matter, and investigating rare alpha decays. An extended R&D was performed to develop advanced quality ZnWO$_4$ crystal scintillators. The R&D programme included the selection of the initial materials, the variation of the compound stoichiometry, the application of single and double crystallization, and the annealing of the crystal boules. The optical transmittance of the produced boules was measured, and the luminescence under X-ray excitation in the temperature region from 85 K to room temperature was studied (thermally stimulated luminescence was measured till 350 K). The energy resolution and the relative scintillation pulse amplitude were measured with gamma-sources demonstrating high scintillation properties of the samples produced by single crystallization from deeply purified zinc and tungsten oxides, with stoichiometric composition, annealed in air atmosphere., Comment: 14 pages; 10 figures

Many low-threshold experiments observe sharply rising event rates of yet unknown origins below a few hundred eV, and larger than expected from known backgrounds. Due to the significant impact of this excess on the dark matter or neutrino sensitivity of these experiments, a collective effort has been started to share the knowledge about the individual observations. For this, the EXCESS Workshop was initiated. In its first iteration in June 2021, ten rare event search collaborations contributed to this initiative via talks and discussions. The contributing collaborations were CONNIE, CRESST, DAMIC, EDELWEISS, MINER, NEWS-G, NUCLEUS, RICOCHET, SENSEI and SuperCDMS. They presented data about their observed energy spectra and known backgrounds together with details about the respective measurements. In this paper, we summarize the presented information and give a comprehensive overview of the similarities and differences between the distinct measurements. The provided data is furthermore publicly available on the workshop's data repository together with a plotting tool for visualization., Comment: 44 pages, 20 figures; Editors: A. Fuss, M. Kaznacheeva, F. Reindl, F. Wagner; updated copyright statements and funding information

The NUCLEUS experiment aims to measure coherent elastic neutrino nucleus scattering of reactor anti-neutrinos using cryogenic calorimeters. Operating at an overburden of 3 m.w.e., muon-induced backgrounds are expected to be one of the dominant background contributions. Besides a high efficiency to identify muon events passing the experimental setup, the NUCLEUS muon veto has to fulfill tight spatial requirements to fit the constraints given by the experimental site and to minimize the induced detector dead-time. We developed highly efficient and compact muon veto modules based on plastic scintillators equipped with wavelength shifting fibers and silicon photo multipliers to collect and detect the scintillation light. In this paper, we present the full characterization of a prototype module with different light read-out configurations. We conclude that an efficient and compact muon veto system can be built for the NUCLEUS experiment from a cube assembly of the developed modules. Simulations show that an efficiency for muon identification of >99 % and an associated rate of 325 Hz is achievable, matching the requirements of the NUCLEUS experiment.