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We show conditional lower bounds for well-studied #P-hard problems: The number of satisfying assignments of a 2-CNF formula with n variables cannot be computed in time exp( o ( n )), and the same is true for computing the number of all independent sets in an n -vertex graph. The permanent of an n × n matrix with entries 0 and 1 cannot be computed in time exp( o ( n )). The Tutte polynomial of an n -vertex multigraph cannot be computed in time exp( o ( n )) at most evaluation points ( x , y ) in the case of multigraphs, and it cannot be computed in time exp( o ( n /poly log n )) in the case of simple graphs. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n -variable 3-CNF formulas cannot be decided in time exp( o ( n )). We relax this hypothesis by introducing its counting version #ETH; namely, that the satisfying assignments cannot be counted in time exp( o ( n )). In order to use #ETH for our lower bounds, we transfer the sparsification lemma for d -CNF formulas to the counting setting.

Excited states in the $T_z=-1$ nucleus $^{70}$Kr have been populated using inelastic scattering of a radioactive $^{70}$Kr beam as well as one- and two-neutron removal reactions from $^{71,72}$Kr at intermediate beam energies. The level scheme of $^{70}$Kr was constructed from the observed $��$-ray transitions and coincidences. Tentative spin and parity assignments were made based on comparison with the mirror nucleus $^{70}$Se. A second $2^+$ state and a candidate for the corresponding $4^+_2$ state suggest shape coexistence in $^{70}$Kr. accepted Phys. Lett. B

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features. 11 pages, 23 plots in 11 figures; some comments and references added, some axis labels corrected; journal version

A nucleoside bearing a solvatochromic push-pull fluorene fluorophore (dC(FL)) was designed and synthesized by the Sonogashira coupling of alkyne-linked fluorene 8 with 5-iodo-2'-deoxycytidine. The fluorene building block 8 and labeled nucleoside dC(FL) exerted bright fluorescence with significant solvatochromic effect providing emission maxima ranging from 421 to 544 nm and high quantum yields even in highly polar solvents, including water. The solvatochromism of 8 was studied by DFT and ADC(2) calculations to show that, depending on the polarity of the solvent, emission either from the planar or the twisted conformation of the excited state can occur. The nucleoside was converted to its triphosphate variant dC(FL)TP which was found to be a good substrate for DNA polymerases suitable for the enzymatic synthesis of oligonucleotide or DNA probes by primer extension or PCR. The fluorene-linked DNA can be used as fluorescent probes for DNA-protein (p53) or DNA-lipid interactions, exerting significant color changes visible even to the naked eye. They also appear to be suitable for time-dependent fluorescence shift studies on DNA, yielding information on DNA hydration and dynamics.

Abstract The carbon and land footprint of 26 certified food products – geographical indications and organic products and their conventional references are assessed. This assessment goes beyond existing literature by (1) designing a calculation method fit for the comparison between certified food and conventional production, (2) using the same calculation method and parameters for 52 products – 26 Food Quality Schemes and their reference products – to allow for a meaningful comparison, (3) transparently documenting this calculation method and opening access to the detailed results and the underlying data, and (4) providing the first assessment of the carbon and land footprint of geographical indications. The method used is Life Cycle Assessment, largely relying on the Cool Farm Tool for the impact assessment. The most common indicator of climate impact, the carbon footprint expressed per ton of product, is not significantly different between certified foods and their reference products. The only exception to this pattern are vegetal organic products, whose carbon footprint is 16% lower. This is because the decrease in greenhouse gas emissions from the absence of mineral fertilizers is never fully offset by the associated lower yield. The climate impact of certified food per hectare is however 26% than their reference and their land footprint is logically 24% higher. Technical specifications directly or indirectly inducing a lower use of mineral fertilizers are a key driver of this pattern. So is yield, which depends both on terroir and farming practices. Overall, this assessment reinforces the quality policy of the European Union: promoting certified food is not inconsistent with mitigating climate change.

The s-process nucleosynthesis in Asymptotic giant branch (AGB) stars depends on the modeling of convective boundaries. We present models and s-process simulations that adopt a treatment of convective boundaries based on the results of hydrodynamic simulations and on the theory of mixing due to gravity waves in the vicinity of convective boundaries. Hydrodynamics simulations suggest the presence of convective boundary mixing (CBM) at the bottom of the thermal pulse-driven convective zone. Similarly, convection-induced mixing processes are proposed for the mixing below the convective envelope during third dredge-up (TDU), where the ${}^{13}{\rm{C}}$ pocket for the s process in AGB stars forms. In this work, we apply a CBM model motivated by simulations and theory to models with initial mass M = 2 and $M=3\,{M}_{\odot }$, and with initial metal content Z = 0.01 and Z = 0.02. As reported previously, the He-intershell abundances of ${}^{12}{\rm{C}}$ and ${}^{16}{\rm{O}}$ are increased by CBM at the bottom of the pulse-driven convection zone. This mixing is affecting the ${}^{22}\mathrm{Ne}$(α, n)${}^{25}\mathrm{Mg}$ activation and the s-process efficiency in the ${}^{13}{\rm{C}}$-pocket. In our model, CBM at the bottom of the convective envelope during the TDU represents gravity wave mixing. Furthermore, we take into account the fact that hydrodynamic simulations indicate a declining mixing efficiency that is already about a pressure scale height from the convective boundaries, compared to mixing-length theory. We obtain the formation of the ${}^{13}{\rm{C}}$-pocket with a mass of $\approx {10}^{-4}\,\,{M}_{\odot }$. The final s-process abundances are characterized by $0.36\lt [{\rm{s}}/\mathrm{Fe}]\lt 0.78$ and the heavy-to-light s-process ratio is $-0.23\lt [\mathrm{hs}/\mathrm{ls}]\lt 0.45$. Finally, we compare our results with stellar observations, presolar grain measurements and previous work.

Hippocampal activity patterns representing movement trajectories are reactivated in immobility and sleep periods, a process associated with memory recall, consolidation, and decision making. It is thought that only fixed, behaviorally relevant patterns can be reactivated, which are stored across hippocampal synaptic connections. To test whether some generalized rules govern reactivation, we examined trajectory reactivation following non-stereotypical exploration of familiar open-field environments. We found that random trajectories of varying lengths and timescales were reactivated, resembling that of Brownian motion of particles. The animals’ behavioral trajectory did not follow Brownian diffusion demonstrating that the exact behavioral experience is not reactivated. Therefore, hippocampal circuits are able to generate random trajectories of any recently active map by following diffusion dynamics. This ability of hippocampal circuits to generate representations of all behavioral outcome combinations, experienced or not, may underlie a wide variety of hippocampal-dependent cognitive functions such as learning, generalization, and planning.

The recent discovery of gravitational waves has opened new horizons for physics. Current and upcoming missions, such as LIGO, VIRGO, KAGRA, and LISA, promise to shed light on black holes of every size from stellar mass (SBH) sizes up to supermassive black holes which reside in galactic nuclei. The intermediate mass black hole (IMBH) family has not been detected beyond any reasonable doubt neither directly nor indirectly. Recent analyses suggest observational evidence for the presence of IMBHs in the centers of two Galactic globular clusters. In this paper, we investigate the possibility that globular clusters were born with a central IMBH, which undergo repeated merger events with SBHs in the cluster core. By means of a semi-analytical method, we follow the evolution of the primordial cluster population in the galactic potential and the Gravitational Wave (GW) mergers of the binary IMBH-SBH systems. Our models predict ≈1000 IMBHs within 1 kpc from the Galactic Center. Our results show that the IMBH-SBH merger rate density changes from \(\mathcal{R} \approx 1000\,\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}\) beyond \(z\approx 2\) to \(\mathcal{R} \approx 1-10\,\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}\) at \(z\approx 0\). The rates at low redshifts may be significantly higher if young massive star clusters host IMBHs. The merger rates are dominated by IMBHs with masses between \(10^3-10^4\,\mathrm{M}_{\odot}\). Currently there are no LIGO/VIRGO upper limits for GW sources in this mass range, but our results show that at design sensitivity these instruments may detect these IMBH-SBH mergers in the coming years. LISA and the Einstein Telescope will be best suited to detect these GW events. The inspirals of IMBH-SBH systems may also generate an unresolved GW background.