La filosofía política de comte y su proyecto social

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Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

Heraldic seizure

AbstractBackground: The term heraldic seizures indicates epileptic seizures caused by cerebrovascular disease, believed to be triggered by silent ischemia and occurring before a stroke. This fact widens the spectrum of possible interrelations between epilepsy and cerebrovascular disease outside the well known context of post-stroke epilepsy. Methods: This is a case report of a healthy 67-year-old male who had a new onset epileptic seizure prior to a lobar intracerebral hemorrhage (ICH). This man began to suffer myoclonic jerks in his left arm which progressed to a generalized tonic–clonic seizure. At the emergency area the physical and neurological examination were unremarkable and a CT scan was normal. The next day the patient developed left hemiparesis, hemianopsia and confusion and a new CT scan showed right parietal–occipital ICH. Conclusions: This case report exemplifies the concept of heraldic seizures, showing a patient who had a focal seizure preceding an intracerebral hemorrhage. Our etiologic diagnostic work led us to a diagnosis of probable amyloid angiopathy. We suggest that cerebral amyloid angiopathy (CAA) may be the underlying cause, since it may be the origin of both the late event (ICH) and the heralding seizures, resulting from concurrent ischemia

On the Dirac delta as initial condition for nonlinear Schr\"odinger equations

In this article we will study the initial value problem for some Schr\"odinger equations with Diraclike initial data and therefore with infinite L2 mass, obtaining positive results for subcritical nonlinearities. In the critical case and in one dimension we prove that after some renormalization the corresponding solution has finite energy. This allows us to conclude a stability result in the defocusing setting. These problems are related to the existence of a singular dynamics for Schr\"odinger maps through the so called Hasimoto transformation.Comment: 17 pages, to appear in in AnIHP Ann Non Li

Universal features of electron-phonon interactions in atomic wires

The effect of electron-phonon interactions in the conductance through metallic atomic wires is theoretically analyzed. The proposed model allows to consider an atomic size region electrically and mechanically coupled to bulk electrodes. We show that under rather general conditions the features due to electron-phonon coupling are described by universal functions of the system transmission coefficients. It is predicted that the reduction of the conductance due to electron-phonon coupling which is observed close to perfect transmission should evolve into an enhancement at low transmission. This crossover can be understood in a transparent way as arising from the competition between elastic and inelastic processes.Comment: 5 pages, 5 figure

First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

Association between sleep-disordered breathing and breast cancer aggressiveness

Background Sleep-disordered breathing (SDB) has been associated with cancer aggressiveness, but studies focused on specific tumors are lacking. In this pilot study we investigated whether SDB is associated with breast cancer (BC) aggressiveness. Methods 83 consecutive women <65 years diagnosed with primary BC underwent a home respiratory polygraphy. Markers of SDB severity included the apnea-hypopnea index (AHI) and the 4% oxygen desaturation index (ODI4). The Ki67 proliferation index, lack of hormone receptors (HR-), Nottingham Histological Grade (NHG), and tumor stage were used as markers of BC aggressiveness. The association between SDB and molecular subtypes of BC was also assessed. Results The mean (SD) age was 48.8 (8.8) years and body mass index was 27.4 (5.4) Kg/m2. 42 women (50.6%) were post-menopausal. The median (IQR) AHI was 5.1 (2–9.4), and ODI4 was 1.5 (0.5–5.8). The median (IQR) AHI did not differ between the groups with Ki67>28% and Ki6728% and Ki67<29% (51.2% vs 52.3%, p = 0.90), HR- and HR+ (58.3% vs 49.1%, p = 0.47), NHG categories (p = 0.89), different tumor stages (p = 0.71), or molecular subtypes (p = 0.73). These results did not change when the ODI4 was used instead of the AHI. Conclusion Our results do not support an association between the presence or severity of SDB and BC aggressiveness.Asociación de Neumología y Cirugía Torácica del Sur (NEUMOSUR) 1/201