Packing identical simple polygons is NP-hard

Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is presented where a small polygon is constructed to encode the entire circuit

The Evolution of Income Composition Inequality in Italy, 1989–2016

We study the evolution of inequality in income composition in terms of capital and labor income in Italy between 1989 and 2016. We document a rise in the share of capital income accruing to the bottom of the distribution, while the top of the distribution increases its share of labor income. This implies a falling degree of income composition inequality in the period considered and a weaker relationship between the functional and personal distribution of income in Italy. This result is robust to various specifications of self-employment income; nonetheless, it hinges crucially on the treatment of rental incomes. While the dynamics of imputed rents has brought about a more equitable distribution of capital incomes across the income distribution, that of actual rents has led to higher concentration of capital incomes at the top in the decade preceding the outbreak of the financial crisis. Finally, we conceptualize a rule of thumb for policy makers seeking to reduce income inequality in the long run

Unilateral spatial neglect after stroke: Current insights

INTRODUCTION: Unilateral spatial neglect (USN) is a disorder of contralesional space awareness which often follows unilateral brain lesion. Since USN impairs awareness of contralesional space/body and often of concomitant motor disorders, its presence represents a negative prognostic factor of functional recovery. Thus, the disorder needs to be carefully diagnosed and treated. Here, we attempted to present a clear and concise picture of current insights in the comprehension and rehabilitation of USN. METHODS: We first provided an updated overview of USN clinical and neuroanatomical features and then highlighted recent progresses in the diagnosis and rehabilitation of the disease. In relation to USN rehabilitation, we conducted a MEDLINE literature research on three of the most promising interventions for USN rehabilitation: prismatic adaptation (PA), non-invasive brain stimulation (NIBS), and virtual reality (VR). The identified studies were classified according to the strength of their methods. RESULTS: The last years have witnessed a relative decrement of interest in the study of neuropsychological disorders of spatial awareness in USN, but a relative increase in the study of potential interventions for its rehabilitation. Although optimal protocols still need to be defined, high-quality studies have demonstrated the efficacy of PA, TMS and tDCS interventions for the treatment of USN. In addition, preliminary investigations are suggesting the potentials of GVS and VR approaches for USN rehabilitation. CONCLUSION: Advancing neuropsychological and neuroscience tools to investigate USN pathophysiology is a necessary step to identify effective rehabilitation treatments and to foster our understanding of neurofunctional bases of spatial cognition in the healthy brain

Riccati-parameter solutions of nonlinear second-order ODEs

It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a `growth' parameter from the trivial null solution up to the particular solution found through the factorization procedureComment: 5 pages, 3 figures, change of title and more tex

The Basilicata Wealth Fund: Resource Policy and Long-Run Economic Development in Southern Italy

This paper contributes to the growing political economy literature of within-country natural resources management, by proposing a new resource policy for the oil-rich southern Italian region of Basilicata. The policy proposal is to establish a (regional) wealth fund in which all the royalty revenues from non-renewable natural resource exploitation in Basilicata would be stored and fully converted into low-risk financial assets. The scope is to give priority to long-run investments as to better exploit revenues from large-scale extraction of natural capital. Establishing a wealth fund at the regional sub-national level is a novel approach that can be applied to other resource-rich regions in the world. I label the fund as the Basilicata Wealth Fund (BWF). The BWF would be a regionally owned investment fund, however independently administered from national authorities (for instance, as an independent legal entity under the jurisdiction of the Bank of Italy). In addition, the paper posits a transparent and clear-cut spending fiscal rule in order to let regional authorities use the resource revenues to finance economic policy. The clear advantage from the BWF would be the stronger focus on long-run economic development and the higher accountability, hence avoiding misuse of resource revenues for myopic fiscal spending

The skirted island : the effect of topography on the flow around planetary scale islands

Author Posting. © Sears Foundation for Marine Research, 2009. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 67 (2009): 435-478, doi:10.1357/002224009790741085.The flow around planetary scale islands is examined when the island possesses a topographic skirt representing a steep continental shelf. The model is barotropic and governed by the shallow water equations and the motion is driven by a wind stress with a constant curl. The presence of the strong topographic "skirt" around the island vitiates the elegant Island Rule of Godfrey and the closed potential vorticity contours around the island produced by the topography allow a geostrophic, stationary mode to resonate with an amplitude that is limited only by dissipation. In the limit of weak forcing the outline of the outermost closed potential vorticity isoline essentially replaces the island shape and determines the flow beyond that contour. Stronger nonlinearity produces substantial changes in the flow pattern as well as the transports trapped on the closed contours and the transport between the island and the basin boundary. Laboratory experiments, numerical calculations and analytical results are presented describing the structure of the flow. A western standing meander at the edge of the island's topography involves a rapid change in the direction of flow and this feature, predicted by analytical and numerical calculations is confirmed in laboratory experiments. As the measure of nonlinearity is increased beyond a threshold that depends on the ratio of the inertial boundary layer thickness to the Munk layer thickness the flow becomes time dependent and a strong eddy field emerges. The transports on the closed contours and the inter-basin exchange outside the closed potential vorticity contours show an enhancement over the linear analytical approximation as nonlinearity increases.This work was supported in part by NSF grant OCE-0451086 (JP) and NSF OCE 05-25729 (KH)

Amino acid substitutions within the heptad repeat domain 1 of murine coronavirus spike protein restrict viral antigen spread in the central nervous system.

Targeted recombination was carried out to select mouse hepatitis viruses (MHVs) in a defined genetic background, containing an MHV-JHM spike gene encoding either three heptad repeat 1 (HR1) substitutions (Q1067H, Q1094H, and L1114R) or L1114R alone. The recombinant virus, which expresses spike with the three substitutions, was nonfusogenic at neutral pH. Its replication was significantly inhibited by lysosomotropic agents, and it was highly neuroattenuated in vivo. In contrast, the recombinant expressing spike with L1114R alone mediated cell-to-cell fusion at neutral pH and replicated efficiently despite the presence of lysosomotropic agents; however, it still caused only subclinical morbidity and no mortality in animals. Thus, both recombinant viruses were highly attenuated and expressed viral antigen which was restricted to the olfactory bulbs and was markedly absent from other regions of the brains at 5 days postinfection. These data demonstrate that amino acid substitutions, in particular L1114R, within HR1 of the JHM spike reduced the ability of MHV to spread in the central nervous system. Furthermore, the requirements for low pH for fusion and viral entry are not prerequisites for the highly attenuated phenotype

On the rate of convergence of the Hamiltonian particle-mesh method

The Hamiltonian Particle-Mesh (HPM) method is a particle-in-cell method for compressible fluid flow with Hamiltonian structure. We present a numer- ical short-time study of the rate of convergence of HPM in terms of its three main governing parameters. We find that the rate of convergence is much better than the best available theoretical estimates. Our results indicate that HPM performs best when the number of particles is on the order of the number of grid cells, the HPM global smoothing kernel has fast decay in Fourier space, and the HPM local interpolation kernel is a cubic spline

Apelin-13 Increases Functional Connexin-43 through Autophagy Inhibition via AKT/mTOR Pathway in the Non-Myocytic Cell Population of the Heart

Studies have shown a link between the downregulation of connexin 43 (Cx43), the predominant isoform in cardiac gap junctions, and high susceptibility to cardiac arrhythmias and cardiomyocyte death. Non-myocytic cells (NMCs), the most abundant component of the heart, exert multiple cardiac functions and represent an important therapeutic target for diseased cardiac tissue. A few studies have investigated the effect of Apelin-13, an endogenous peptide with a key role in various cardiovascular functions, on Cx43 expression in cardiomyocytes. However, it remained unknown whether Apelin-13 influences Cx43 expression in NMCs. Here, we found that in NMCs, Cx43 protein expression increased after Apelin-13 treatment (100 nM for 48 h). Furthermore, dye transfer assays proved that Apelin-13-treated NMCs had a greater ability to communicate with surrounding cardiomyocytes, and this effect was abrogated by carbenoxolone, a gap junction inhibitor. Interestingly, we showed that Apelin-13 increased Cx43 through autophagy inhibition, as proved by the upregulation of p62 and LC3I, acting as 3-MA, a well-known autophagy inhibitor. In addition, Apelin-13-induced AKT and mTOR phosphorylation was abolished by LY294002 and rapamycin inhibitors resulting in Cx43 increased suppression. These results open the possibility of targeting gap junctions in NMCs with Apelin-13 as an exciting therapeutic approach with great potential

A Static Optimality Transformation with Applications to Planar Point Location

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All these methods suffer from the requirement that the query distribution must be known in advance. We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but it requires no prior information about the queries. This is a 2D analogue of the jump from Knuth's optimum binary search trees (discovered in 1971) to the splay trees of Sleator and Tarjan in 1985. While the former need to know the query distribution, the latter are statically optimal. This means that we can adapt to the query sequence and achieve the same asymptotic performance as an optimum static structure, without needing any additional information.Comment: 13 pages, 1 figure, a preliminary version appeared at SoCG 201