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This paper surveys the landscape of security and data attacks on machine unlearning, with a focus on financial and e-commerce applications. We discuss key privacy threats such as Membership Inference Attacks and Data Reconstruction Attacks, where adversaries attempt to infer or reconstruct data that should have been removed. In addition, we explore security attacks including Machine Unlearning Data Poisoning, Unlearning Request Attacks, and Machine Unlearning Jailbreak Attacks, which target the underlying mechanisms of unlearning to manipulate or corrupt the model. To mitigate these risks, various defense strategies are examined, including differential privacy, robust cryptographic guarantees, and Zero-Knowledge Proofs (ZKPs), offering verifiable and tamper-proof unlearning mechanisms. These approaches are essential for safeguarding data integrity and privacy in high-stakes financial and e-commerce contexts, where compromised models can lead to fraud, data leaks, and reputational damage. This survey highlights the need for continued research and innovation in secure machine unlearning, as well as the importance of developing strong defenses against evolving attack vectors.

We introduce a formal theory called Flow where the intended interpretation of its terms is that of function. We prove ZF, ZFC and ZFU (ZF with atoms) can be immersed within Flow as natural consequences from our framework. Our first important application is the introduction of a model of ZFU where the Partition Principle holds but the Axiom of Choice fails, if Flow is consistent. So, our framework allows us to address the oldest open problem in set theory: if the Partition Principle entails the Axiom of Choice., Comment: 44 pages, 3 figures, 2 tables. This is a fully revised version of a previous work. arXiv admin note: substantial text overlap with arXiv:2010.03664

We introduce a general theory of functions called Flow. We prove ZF, non-well founded ZF and ZFC can be immersed within Flow as a natural consequence from our framework. The existence of strongly inaccessible cardinals is entailed from our axioms. And our first important application is the introduction of a model of Zermelo-Fraenkel set theory where the Partition Principle (PP) holds but not the Axiom of Choice (AC). So, Flow allows us to answer to the oldest open problem in set theory: if PP entails AC., Comment: 37 pages, 4 Figures

Using the idea of the instanton approach to quantum tunneling we try to obtain a method of calculating spontaneous fission rates for nuclei with the odd number of neutrons or protons. This problem has its origin in the failure of the adiabatic cranking approximation which serves as the basis in calculations of fission probabilities. Selfconsistent instanton equations, with and without pairing, are reviewed and then simplified to non-selfconsistent versions with phenomenological single-particle potential and seniority pairing interaction. Solutions of instanton-like equations without pairing and actions they produce are studied for the Woods-Saxon potential along realistic fission trajectories. Actions for unpaired particles are combined with cranking actions for even-even cores and fission hindrance for odd-A nuclei is studied in such a hybrid model. With the assumed equal mass parameters for neighbouring odd-A and even-even nuclei, the model shows that freezing the K {\pi} configuration leads to a large overestimate of the fission hindrance factors. Actions with adiabatic configurations mostly show not enough hindrance; instanton-like actions for blocked nucleons correct this, but not sufficiently., Comment: 33 pages, 15 figures

After shortly analyzing data relevant to fission hindrance of odd-A nuclei and high-$K$ isomers in superheavy (SH) region we point out the inconsistency of current fission theory and propose an approach based on the instanton formalism. A few results of this method, simplified by replacing selfconsistency by elements of the macro-micro model, are given to illustrate its features., Comment: Contribution to Proceedings of the XXXV Mazurian Lakes Conference on Physics, Piaski, Poland, September 3-9, 2017

The \MJ\ Collaboration is operating an array of high purity Ge detectors to search for neutrinoless double-beta decay in $^{76}$Ge. The \MJ\ \DEM\ comprises 44.1~kg of Ge detectors (29.7 kg enriched in $^{76}$Ge) split between two modules contained in a low background shield at the Sanford Underground Research Facility in Lead, South Dakota. Here we present results from data taken during construction, commissioning, and the start of full operations. We achieve unprecedented energy resolution of 2.5 keV FWHM at \qval\ and a very low background with no observed candidate events in 10 kg yr of enriched Ge exposure, resulting in a lower limit on the half-life of $1.9\times10^{25}$ yr (90\% CL). This result constrains the effective Majorana neutrino mass to below 240 to 520 meV, depending on the matrix elements used. In our experimental configuration with the lowest background, the background is $4.0_{-2.5}^{+3.1}$ counts/(FWHM t yr)., Comment: typos fixed

The IGEX experiment has been operating enriched germanium detectors in the Canfranc Underground Laboratory (Spain) in a search for the neutrinoless double decay of 76Ge. The implementation of Pulse Shape Discrimination techniques to reduce the radioactive background is described in detail. This analysis has been applied to a fraction of the IGEX data, leading to a rejection of ~60 % of their background, in the region of interest (from 2 to 2.5 MeV), down to ~0.09 c/(keV kg y)., Comment: 18 pages, 10 figures

One IGEX 76Ge double-beta decay detector is currently operating in the Canfranc Underground Laboratory in a search for dark matter WIMPs, through the Ge nuclear recoil produced by the WIMP elastic scattering. In this talk we report on the on-going efforts to understand and eventually reject the background at low energy. These efforts have led to the improvement of the neutron shielding and to partial reduction of the background, but still the remaining events are not totally identified. A tritium contamination or muon-induced neutrons are considered as possible sources, simulations and experimental test being still under progress. According to the success of this study we comment the prospects of the experiment as well as those of its future extension, the GEDEON dark matter experiment., Comment: 6 pages, 3 figures, talk given at 4th International Workshop on the Identification of Dark Matter, York, September 2002

The International Germanium Experiment (IGEX) has analyzed 117 mole yr of 76Ge data from its isotopically enriched (86% 76Ge) germanium detectors. Applying pulse-shape discrimination (PSD) to the more recent data, the lower bound on the half-life for neutrinoless double-beta decay of 76Ge is: $T_{1/2}(0\nu)> 1.57 \times 10^{25}$ yr (90% C.L.). This corresponds to an upper bound in the Majorana neutrino mass parameter,$$, between 0.33 eV and 1.35 eV, depending on the choice of theoretical nuclear matrix elements used in the analysis.

We comment on the recent claim for the experimental observation of neutrinoless double-beta decay. We discuss several limitations in the analysis provided in that paper and conclude that there is no basis for the presented claim., Comment: A comment written to Modern Physics Letters A. 4 pages, no figures. Updated version, accepted for publication

The Majorana Experiment is a next-generation Ge-76 double-beta decay search. It will employ 500 kg of Ge, isotopically enriched to 86% in Ge-76, in the form of 200 detectors in a close-packed array for high granularity. Each crystal will be electronically segmented, with each region fitted with pulse-shape analysis electronics. A half-life sensitivity is predicted of 4.2e27 y or < 0.02-0.07 eV, depending on the nuclear matrix elements used to interpret the data., Comment: 13 pages, 4 figures. Presented by F. T. Avignone at NANP 2001

One IGEX 76Ge double-beta decay detector is currently operating in the Canfranc Underground Laboratory in a search for dark matter WIMPs, through the Ge nuclear recoil produced by the WIMP elastic scattering. A new exclusion plot has been derived for WIMP-nucleon spin-independent interactions. To obtain this result, 40 days of data from the IGEX detector (energy threshold 4 keV), recently collected, have been analyzed. These data improve the exclusion limits derived from all the other ionization germanium detectors in the mass region from 20 GeV to 200 GeV, where a WIMP supposedly responsible for the annual modulation effect reported by the DAMA experiment would be located. The new IGEX exclusion contour enters, by the first time, the DAMA region by using only raw data, with no background discrimination, and excludes its upper left part. It is also shown that with a moderate improvement of the detector performances, the DAMA region could be fully explored., Comment: 3 pages, 3 figures, talk delivered at the 7th International Workshop on Topics in Astroparticle and Underground Physics (TAUP 2001), September 2001, Laboratori Nazionali del Gran Sasso, Italy (to appear in the Conference Proceedings, Nucl. Phys. B (Proc. Suppl.))

One IGEX 76Ge double-beta decay detector is currently operating in the Canfranc Underground Laboratory in a search for dark matter WIMPs, through the Ge nuclear recoil produced by the WIMP elastic scattering. A new exclusion plot, has been derived for WIMP-nucleon spin-independent interactions. To obtain this result, 40 days of data from the IGEX detector (energy threshold E \~ 4 keV), recently collected, have been analyzed. These data improve the exclusion limits derived from all the other ionization germanium detectors in the mass region from 20 GeV to 200 GeV, where a WIMP supposedly responsible for the annual modulation effect reported by the DAMA experiment would be located. The new IGEX exclusion contour enters, by the first time, the DAMA region by using only raw data, with no background discrimination, and excludes its upper left part. It is also shown that with a moderate improvement of the detector performances, the DAMA region could be fully explored., Comment: 14 pages, 8 figures, submitted to Physics Letters B (revised version after referee's comments, some figures added)

A small, natural abundance, germanium detector (COSME) has been operating recently at the Canfranc Underground Laboratory (Spanish Pyrenees) in improved conditions of shielding and overburden with respect to a previous operation of the same detector. An exposure of 72.7 kg day in these conditions has at present a background improvement of about one order of magnitude compared to the former operation of the detector. These new data have been applied to a direct search for WIMPs and solar axions. New WIMP exclusion plots improving the current bounds for low masses are reported. The paper also presents a limit on the axion-photon coupling obtained from the analysis of the data looking for a Primakoff axion-to-photon conversion and Bragg scattering inside the crystal., Comment: LaTeX, 11 pages, 4 figures, submitted to Astropart. Phys

Two germanium detectors are currently operating in the Canfranc Underground Laboratory at 2450 m.w.e looking for WIMP dark matter. One is a 2 kg 76Ge IGEX detector (RG-2) which has an energy threshold of 4 keV and a low-energy background rate of about 0.3 c/keV/kg/day. The other is a small (234 g) natural abundance Ge detector (COSME), of low energy threshold (2.5 keV) and an energy resolution of 0.4 keV at 10 keV which is looking for WIMPs and for solar axions. The analysis of 73 kg-days of data taken by COSME in a search for solar axions via their photon Primakoff conversion and Bragg scattering in the Ge crystal yields a 95% C.L. limit for the axion-photon coupling g < 2.8 10^-9 GeV^-1. These data, analyzed for WIMP searches provide an exclusion plot for WIMP-nucleon spin-independent interaction which improves previous plots in the low mass region. On the other hand, the exclusion plot derived from the 60 kg-days of data from the RG-2 IGEX detector improves the exclusion limits derived from other ionization (non thermal) germanium detector experiments in the region of WIMP masses from 30 to 100 GeV recently singled out by the reported DAMA annual modulation effect., Comment: 6 pages, talk given at IDM2000, York, September 2000

The IGEX Collaboration enriched 76Ge double-beta decay detectors are currently operating in the Canfranc Underground Laboratory with an overburden of 2450 m.w.e. A recent upgrade has made it possible to use them in a search for WIMPs. A new exclusion plot has been derived for WIMP-nucleon spin-independent interaction. To obtain this result, 30 days of data from one IGEX detector, which has an energy threshold of ~4 keV, have been considered. These data improve the exclusion limits derived from other germanium diode experiments in the ~50 GeV DAMA region, and show that with a moderate improvement of the background below 10 keV, the DAMA region may be tested with an additional 1 kg-year of exposure., Comment: 7 pages, 2 figures, submitted to Physics Letters

Data collected during three years with a germanium spectrometer at the Sierra Grande underground laboratory have been analyzed for distinctive features of annual modulation of the signal induced by WIMP dark matter candidates. The main motivation for this analysis was the recent suggestion by the DAMA/NaI Collaboration that a yearly modulation signal could not be rejected at the 90% confidence level when analyzing data obtained with a high-mass low-background scintillator detector. We performed two different analyses of the data: First, the statistical distribution of modulation-significance variables (expected from an experiment running under the conditions of Sierra Grande) was compared with the same variables obtained from the data. Second, the data were analyzed in energy bins as an independent check of the first result and to allow for the possibility of a crossover in the expected signal. In both cases no statistically significant deviation from the null result was found, which could support the hypothesis that the data contain a modulated component. A plot is also presented to enable the comparison of these results to those of the DAMA collaboration., Comment: New version accepted by Astroparticle Physics. Changes suggested by the referee about the theoretical prediction of rates are included. Conclusions remain unaffected. 14 pages, LaTeX, 7 figures. Uses epsfig macro

The 8.4 Tesla, 10 m long transverse magnetic field of a twin aperture LHC bending magnet can be utilized as a macroscopic coherent solar axion-to-photon converter. Numerical calculations show that the integrated time of alignment with the Sun would be 33 days per year with the magnet on a tracking table capable of $\pm 5^o$ in the vertical direction and $\pm 40^o$ in the horizontal direction. The existing lower bound on the axion-to-photon coupling constant can be improved by a factor between 50 and 100 in 3 years, i.e., $g_{a\gamma\gamma} \lesssim 9\cdot 10^{-11} GeV^{-1}$ for axion masses $\lesssim$ 1 eV. This value falls within the existing open axion mass window. The same set-up can simultaneously search for low- and high-energy celestial axions, or axion-like particles, scanning the sky as the Earth rotates and orbits the Sun., Comment: Final version, accepted for publication in Nucl. Instr. Meth. A. More information can be found at http://wwwinfo.cern.ch/~collar/SATAN/alvaro.html

A new technique has been used to search for solar axions using a single crystal germanium detector. It exploits the coherent conversion of axions into photons when their angle of incidence satisfies a Bragg condition with a crystalline plane. The analysis of approximately 1.94 kg.yr of data from the 1-kg DEMOS detector in Sierra Grande, Argentina, yields a new laboratory bound on axion-photon coupling of g_{a,\gamma\gamma}<2.7\times 10^{-9} GeV^{-1} independent of axion mass up to \sim 1 keV., Comment: List of authors now complete. 5 pages (A4), LaTex, 4 PS figures, uses epsf and espcrc2(included) macros. Talk at the 5th International Workshop on ``Topics in Astroparticle and Underground Physics'' (TAUP97), Gran Sasso, Italy, 7-11 September, 1997, to appear in the Proceedings, Nucl. Phys. B(PS), A. Bottino, A. di Credico and P. Monacelli (eds.)

Results are reported of an experimental search for the unique, rapidly varying temporal pattern of solar axions coherently converting into photons via the Primakoff effect in a single crystal germanium detector. This conversion is predicted when axions are incident at a Bragg angle with a crystalline plane. The analysis of approximately 1.94 kg.yr of data from the 1 kg DEMOS detector in Sierra Grande, Argentina, yields a new laboratory bound on axion-photon coupling of $g_{a\gamma \gamma} < 2.7\cdot 10^{-9}$ GeV$^{-1}$, independent of axion mass up to ~ 1 keV., Comment: RevTeX, 11 pages, figures can be obtained by fax from Juan.Collar@cern.ch. Submitted to Phys. Lett. B