Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs

Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we present a possibly simpler proof of the result in [CLNV15] and strengthen the result to show that it is PSPACE-hard to determine the minimum number of pebbles to an additive $n^{1/3-\epsilon}$ term for all $\epsilon > 0$, which improves upon the currently known additive constant hardness of approximation [CLNV15] in the standard pebble game. We also introduce a family of explicit, constant indegree graphs with $n$ nodes where there exists a graph in the family such that using constant $k$ pebbles requires $\Omega(n^k)$ moves to pebble in both the standard and black-white pebble games. This independently answers an open question summarized in [Nor15] of whether a family of DAGs exists that meets the upper bound of $O(n^k)$ moves using constant $k$ pebbles with a different construction than that presented in [AdRNV17].Comment: Preliminary version in WADS 201

Algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei

We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single-particle degrees of freedom in an application to elastic and inelastic proton scattering from $^{195}$Pt.Comment: latex, 14 pages, 4 figures uuencoded, to be published in Physical Review

Environmental and economic benefits from the phase-out of residential oil heating: A study from the Aosta Valley region (Italy)

Although its use is declining, oil heating is still used in areas not covered by the methane grid. Oil heating is becoming more and more expensive, requires frequent tank refill operations, and has high emissions of greenhouse gas (GHG) and air pollutants such as SOx. In addition, spills from oil underground storage tanks (USTs) represent a serious environmental threat to soil and groundwater quality. In this paper, we present a comprehensive analysis on technical alternatives to oil heating with reference to the Aosta Valley (NW Italy), where this fuel is still often used and numerous UST spills have been reported in the last 20 years. We assess operational issues, GHG and pollutant emissions, and unit costs of the heat produced for several techniques: LPG boilers, wood boilers (logs, chips, pellets) and heat pumps (air-source, geothermal closed-loop and open-loop systems). We examine the investment to implement such solutions in two typical cases, a detached house and a block of flats, deriving payback times of about 3–8 years. Wood log boilers turn out to be the most economically convenient solutions; however, heat pumps provide several benefits from the operational and environmental points of view. In addition, including solar thermal panels for domestic hot water or a photovoltaic plant would have payback times of about 6–9 years. The results highlight the economic feasibility and the multiple benefits of a rapid phase-out of oil heating in Italy

A Barren Landscape?

We consider the generation of a non-perturbative superpotential in F-theory compactifications with flux. We derive a necessary condition for the generation of such a superpotential in F-theory. For models with a single volume modulus, we show that the volume modulus is never stabilized by either abelian instantons or gaugino condensation. We then comment on how our analysis extends to a larger class of compactifications. From our results, it appears that among large volume string compactifications, metastable de Sitter vacua (should any exist) are non-generic.Comment: 14 pages, comments adde

Primordial magnetic fields and the HI signal from the epoch of reionization

The implication of primordial magnetic-field-induced structure formation for the HI signal from the epoch of reionization is studied. Using semi-analytic models, we compute both the density and ionization inhomogeneities in this scenario. We show that: (a) The global HI signal can only be seen in emission, unlike in the standard $\Lambda$CDM models, (b) the density perturbations induced by primordial fields, leave distinctive signatures of the magnetic field Jeans' length on the HI two-point correlation function, (c) the length scale of ionization inhomogeneities is \la 1 \rm Mpc. We find that the peak expected signal (two-point correlation function) is $\simeq 10^{-4} \rm K^2$ in the range of scales $0.5\hbox{-}3 \rm Mpc$ for magnetic field strength in the range $5 \times 10^{-10} \hbox{-}3 \times 10^{-9} \rm G$. We also discuss the detectability of the HI signal. The angular resolution of the on-going and planned radio interferometers allows one to probe only the largest magnetic field strengths that we consider. They have the sensitivity to detect the magnetic field-induced features. We show that thefuture SKA has both the angular resolution and the sensitivity to detect the magnetic field-induced signal in the entire range of magnetic field values we consider, in an integration time of one week.Comment: 19 pages, 5 figures, to appear in JCA

Maladaptive striatal plasticity and abnormal reward-learning in cervical dystonia

In monogenetic generalized forms of dystonia, in vitro neurophysiological recordings have demonstrated direct evidence for abnormal plasticity at the level of the cortico‐striatal synapse. It is unclear whether similar abnormalities contribute to the pathophysiology of cervical dystonia, the most common type of focal dystonia. We investigated whether abnormal cortico‐striatal synaptic plasticity contributes to abnormal reward‐learning behavior in patients with focal dystonia. Forty patients and 40 controls performed a reward gain and loss avoidance reversal learning task. Participant's behavior was fitted to a computational model of the basal ganglia incorporating detailed cortico‐striatal synaptic learning rules. Model comparisons were performed to assess the ability of four hypothesized receptor specific abnormalities of cortico‐striatal long‐term potentiation (LTP) and long‐term depression (LTD): increased or decreased D1:LTP/LTD and increased or decreased D2: LTP/LTD to explain abnormal behavior in patients. Patients were selectively impaired in the post‐reversal phase of the reward task. Individual learning rates in the reward reversal task correlated with the severity of the patient's motor symptoms. A model of the striatum with decreased D2:LTP/ LTD best explained the patient's behavior, suggesting excessive D2 cortico‐striatal synaptic depotentiation could underpin biased reward‐learning in patients with cervical dystonia. Reversal learning impairment in cervical dystonia may be a behavioral correlate of D2‐specific abnormalities in cortico‐striatal synaptic plasticity. Reinforcement learning tasks with computational modeling could allow the identification of molecular targets for novel treatments based on their ability to restore normal reward‐learning behavior in these patients