Fast and Simple Modular Subset Sum

We revisit the Subset Sum problem over the finite cyclic group $\mathbb{Z}_m$ for some given integer $m$. A series of recent works has provided asymptotically optimal algorithms for this problem under the Strong Exponential Time Hypothesis. Koiliaris and Xu (SODA'17, TALG'19) gave a deterministic algorithm running in time $\tilde{O}(m^{5/4})$, which was later improved to $O(m \log^7 m)$ randomized time by Axiotis et al. (SODA'19). In this work, we present two simple algorithms for the Modular Subset Sum problem running in near-linear time in $m$, both efficiently implementing Bellman's iteration over $\mathbb{Z}_m$. The first one is a randomized algorithm running in time $O(m\log^2 m)$, that is based solely on rolling hash and an elementary data-structure for prefix sums; to illustrate its simplicity we provide a short and efficient implementation of the algorithm in Python. Our second solution is a deterministic algorithm running in time $O(m\ \mathrm{polylog}\ m)$, that uses dynamic data structures for string manipulation. We further show that the techniques developed in this work can also lead to simple algorithms for the All Pairs Non-Decreasing Paths Problem (APNP) on undirected graphs, matching the asymptotically optimal running time of $\tilde{O}(n^2)$ provided in the recent work of Duan et al. (ICALP'19)

49Cr: Towards full spectroscopy up to 4 MeV

The nucleus 49Cr has been studied analysing gamma-gamma coincidences in the reaction 46Ti(alpha,n)49Cr at the bombarding energy of 12 MeV. The level scheme has been greatly extended at low excitation energy and several new lifetimes have been determined by means of the Doppler Shift Attenuation Method. Shell model calculations in the full pf configuration space reproduce well negative-parity levels. Satisfactory agreement is obtained for positive parity levels by extending the configuration space to include a nucleon-hole either in the 1d3/2 or in the 2s1/2 orbitals. A nearly one-to-one correspondence is found between experimental and theoretical levels up to an excitation energy of 4 MeV. Experimental data and shell model calculations are interpreted in terms of the Nilsson diagram and the particle-rotor model, showing the strongly coupled nature of the bands in this prolate nucleus. Nine values of K(pi) are proposed for the levels observed in this experiment. As a by-result it is shown that the values of the experimental magnetic moments in 1f7/2 nuclei are well reproduced without quenching the nucleon g-factors.Comment: 13 pages, 8 figure

Hindered E4 decay of the 12+ yrast trap in 52Fe

Abstract The γ decay of the 12 + yrast trap in 52Fe has been measured for the first time. The two E4 γ-branches to the 8 + states are hindered with respect to other B ( E 4 ) reduced transition probabilities measured in the f 7 / 2 shell. The interpretation of the data is given in the full pf shell model framework, comparing the results obtained with different residual interactions. It is shown that measurements of hexadecapole transition probabilities constitute a powerful tool in discriminating the correct configuration of the involved wavefunctions

Hindered E4 decay of the 12+ yrast trap in 52Fe

AbstractThe γ decay of the 12+ yrast trap in 52Fe has been measured for the first time. The two E4 γ-branches to the 8+ states are hindered with respect to other B(E4) reduced transition probabilities measured in the f7/2 shell. The interpretation of the data is given in the full pf shell model framework, comparing the results obtained with different residual interactions. It is shown that measurements of hexadecapole transition probabilities constitute a powerful tool in discriminating the correct configuration of the involved wavefunctions

Studies of new Higgs boson interactions through nonresonant HH production in the b¯bγγ fnal state in pp collisions at √s = 13 TeV with the ATLAS detector

A search for nonresonant Higgs boson pair production in the b ¯bγγ fnal state is performed using 140 fb−1 of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. This analysis supersedes and expands upon the previous nonresonant ATLAS results in this fnal state based on the same data sample. The analysis strategy is optimised to probe anomalous values not only of the Higgs (H) boson self-coupling modifer κλ but also of the quartic HHV V (V = W, Z) coupling modifer κ2V . No signifcant excess above the expected background from Standard Model processes is observed. An observed upper limit µHH < 4.0 is set at 95% confdence level on the Higgs boson pair production cross-section normalised to its Standard Model prediction. The 95% confdence intervals for the coupling modifers are −1.4 < κλ < 6.9 and −0.5 < κ2V < 2.7, assuming all other Higgs boson couplings except the one under study are fxed to the Standard Model predictions. The results are interpreted in the Standard Model efective feld theory and Higgs efective feld theory frameworks in terms of constraints on the couplings of anomalous Higgs boson (self-)interactions

Measurement of the total cross section and ρ -parameter from elastic scattering in pp collisions at √s=13 TeV with the ATLAS detector

In a special run of the LHC with β⋆= 2.5 km, proton–proton elastic-scattering events were recorded at s=13 TeV with an integrated luminosity of 340μb-1 using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from - t= 2.5 · 10 - 4 GeV 2 to - t= 0.46 GeV 2 using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section σtot , parameters of the nuclear slope, and the ρ -parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t→ 0 . These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the t-dependence. The results for σtot and ρ are σtot(pp→X)=104.7±1.1mb,ρ=0.098±0.011. The uncertainty in σtot is dominated by the luminosity measurement, and in ρ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude