Optimal sequencing of a set of positive numbers with the variance of the sequence's partial sums maximized

We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that the symmetric problem which aims at minimizing the variance of the same partial sums is proved to be NP-complete in the literature.Comment: 12 pages;Accepted for publication in Optimization Lette

Ground States of Two-Dimensional Polyampholytes

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$, restricted to a 2-dimensional square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We study the ground state properties of the polymers as a function of their excess charge $Q$ for all possible charge sequences up to a polymer length N=18. We find that the ground state of the neutral ensemble is compact and its energy extensive and self-averaging. The addition of small excess charge causes an expansion of the ground state with the monomer density depending only on $Q$. In an annealed ensemble the ground state is fully stretched for any excess charge $Q>0$.Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.

Trait and state interoceptive abnormalities are associated with dissociation and seizure frequency in patients with functional seizures.

OBJECTIVE: Dissociative traits represent a disturbance in selfhood that may predispose to, and trigger, functional seizures (FSs). The predictive representation and control of the internal physiological state of the body (interoception) are proposed to underpin the integrity of the sense of self ("minimal selfhood"). Therefore, discrepancies between objective and subjective aspects of interoception may relate to symptom expression in patients with FSs. Here, we tested whether individual differences in trait measures of interoception relate to dissociative symptoms, and whether state interoceptive deficits predict FS occurrence. METHODS: Forty-one participants with FSs and 30 controls completed questionnaire ratings of dissociation, and measures of (1) interoceptive accuracy (IA)-objective performance on heartbeat detection tasks; (2) trait interoceptive sensibility-subjective sensitivity to internal sensations (using the Porges Body Perception Questionnaire); and (3) state interoceptive sensibility-subjective trial-by-trial measures of confidence in heartbeat detection. Interoceptive trait prediction error (ITPE) was calculated from the discrepancy between IA and trait sensibility, and interoceptive state prediction error (ISPE) from the discrepancy between IA and state sensibility. RESULTS: Patients with FSs had significantly lower IA and greater trait interoceptive sensibility than healthy controls. ITPE was the strongest predictor of dissociation after controlling for trait anxiety and depression in a regression model. ISPE correlated significantly with FS frequency after controlling for state anxiety. SIGNIFICANCE: Patients with FSs have disturbances in interoceptive processing that predict both dissociative traits reflecting the disrupted integrity of self-representation, and the expression of FSs. These findings provide insight into the pathophysiology of functional neurological disorder, and could lead to novel diagnostic and therapeutic approaches

Alternating Electric Fields (Tumor-Treating Fields Therapy) Can Improve Chemotherapy Treatment Efficacy in Non-Small Cell Lung Cancer Both In Vitro and In Vivo

Non-small cell lung cancer (NSCLC) is one of the leading causes of cancer-related deaths worldwide. Common treatment modalities for NSCLC include surgery, radiotherapy, chemotherapy, and, in recent years, the clinical management paradigm has evolved with the advent of targeted therapies. Despite such advances, the impact of systemic therapies for advanced disease remains modest, and as such, the prognosis for patients with NSCLC remains poor. Standard modalities are not without their respective toxicities and there is a clear need to improve both efficacy and safety for current management approaches. Tumor-treating fields (TTFields) are low-intensity, intermediate-frequency alternating electric fields that disrupt proper spindle microtubule arrangement, thereby leading to mitotic arrest and ultimately to cell death. We evaluated the effects of combining TTFields with standard chemotherapeutic agents on several NSCLC cell lines, both in vitro and in vivo. Frequency titration curves demonstrated that the inhibitory effects of TTFields were maximal at 150 kHz for all NSCLC cell lines tested, and that the addition of TTFields to chemotherapy resulted in enhanced treatment efficacy across all cell lines. We investigated the response of Lewis lung carcinoma and KLN205 squamous cell carcinoma in mice treated with TTFields in combination with pemetrexed, cisplatin, or paclitaxel and compared these to the efficacy observed in mice exposed only to the single agents. Combining TTFields with these therapeutic agents enhanced treatment efficacy in comparison with the respective single agents and control groups in all animal models. Together, these findings suggest that combining TTFields therapy with chemotherapy may provide an additive efficacy benefit in the management of NSCLC

The S-Star Cluster at the Center of the Milky Way: On the nature of diffuse NIR emission in the inner tenth of a parsec

Sagittarius A*, the super-massive black hole at the center of the Milky Way, is surrounded by a small cluster of high velocity stars, known as the S-stars. We aim to constrain the amount and nature of stellar and dark mass associated with the cluster in the immediate vicinity of Sagittarius A*. We use near-infrared imaging to determine the $K_\mathrm{s}$-band luminosity function of the S-star cluster members, and the distribution of the diffuse background emission and the stellar number density counts around the central black hole. This allows us to determine the stellar light and mass contribution expected from the faint members of the cluster. We then use post-Newtonian N-body techniques to investigate the effect of stellar perturbations on the motion of S2, as a means of detecting the number and masses of the perturbers. We find that the stellar mass derived from the $K_\mathrm{s}$-band luminosity extrapolation is much smaller than the amount of mass that might be present considering the uncertainties in the orbital motion of the star S2. Also the amount of light from the fainter S-cluster members is below the amount of residual light at the position of the S-star cluster after removing the bright cluster members. If the distribution of stars and stellar remnants is strongly enough peaked near Sagittarius A*, observed changes in the orbital elements of S2 can be used to constrain both their masses and numbers. Based on simulations of the cluster of high velocity stars we find that at a wavelength of 2.2 $\mu$m close to the confusion level for 8 m class telescopes blend stars will occur (preferentially near the position of Sagittarius A*) that last for typically 3 years before they dissolve due to proper motions.Comment: 14 pages, 11 figures, minor changes to match the published version in Astronomy & Astrophysic

The Galactic Center Black Hole Laboratory

The super-massive 4 million solar mass black hole Sagittarius~A* (SgrA*) shows flare emission from the millimeter to the X-ray domain. A detailed analysis of the infrared light curves allows us to address the accretion phenomenon in a statistical way. The analysis shows that the near-infrared flare amplitudes are dominated by a single state power law, with the low states in SgrA* limited by confusion through the unresolved stellar background. There are several dusty objects in the immediate vicinity of SgrA*. The source G2/DSO is one of them. Its nature is unclear. It may be comparable to similar stellar dusty sources in the region or may consist predominantly of gas and dust. In this case a particularly enhanced accretion activity onto SgrA* may be expected in the near future. Here the interpretation of recent data and ongoing observations are discussed.Comment: 30 pages - 7 figures - accepted for publication by Springer's "Fundamental Theories of Physics" series; summarizing GC contributions of 2 conferences: 'Equations of Motion in Relativistic Gravity' at the Physikzentrum Bad Honnef, Bad Honnef, Germany, (Feb. 17-23, 2013) and the COST MP0905 'The Galactic Center Black Hole Laboratory' Granada, Spain (Nov. 19 - 22, 2013

Star Formation and Dynamics in the Galactic Centre

The centre of our Galaxy is one of the most studied and yet enigmatic places in the Universe. At a distance of about 8 kpc from our Sun, the Galactic centre (GC) is the ideal environment to study the extreme processes that take place in the vicinity of a supermassive black hole (SMBH). Despite the hostile environment, several tens of early-type stars populate the central parsec of our Galaxy. A fraction of them lie in a thin ring with mild eccentricity and inner radius ~0.04 pc, while the S-stars, i.e. the ~30 stars closest to the SMBH (<0.04 pc), have randomly oriented and highly eccentric orbits. The formation of such early-type stars has been a puzzle for a long time: molecular clouds should be tidally disrupted by the SMBH before they can fragment into stars. We review the main scenarios proposed to explain the formation and the dynamical evolution of the early-type stars in the GC. In particular, we discuss the most popular in situ scenarios (accretion disc fragmentation and molecular cloud disruption) and migration scenarios (star cluster inspiral and Hills mechanism). We focus on the most pressing challenges that must be faced to shed light on the process of star formation in the vicinity of a SMBH.Comment: 68 pages, 35 figures; invited review chapter, to be published in expanded form in Haardt, F., Gorini, V., Moschella, U. and Treves, A., 'Astrophysical Black Holes'. Lecture Notes in Physics. Springer 201

Alternating electric fields (TTFields) inhibit metastatic spread of solid tumors to the lungs

Tumor treating fields (TTFields) are low intensity, intermediate frequency, alternating electric fields used to treat cancerous tumors. This novel treatment modality effectively inhibits the growth of solid tumors in vivo and has shown promise in pilot clinical trials in patients with advanced stage solid tumors. TTFields were tested for their potential to inhibit metastatic spread of solid tumors to the lungs in two animal models: (1) Mice injected with malignant melanoma cells (B16F10) into the tail vein, (2) New Zealand White rabbits implanted with VX-2 tumors within the kidney capsule. Mice and rabbits were treated using two-directional TTFields at 100–200 kHz. Animals were either monitored for survival, or sacrificed for pathological and histological analysis of the lungs. The total number of lung surface metastases and the absolute weight of the lungs were both significantly lower in TTFields treated mice then in sham control mice. TTFields treated rabbits survived longer than sham control animals. This extension in survival was found to be due to an inhibition of metastatic spread, seeding or growth in the lungs of TTFields treated rabbits compared to controls. Histologically, extensive peri- and intra-tumoral immune cell infiltration was seen in TTFields treated rabbits only. These results raise the possibility that in addition to their proven inhibitory effect on the growth of solid tumors, TTFields may also have clinical benefit in the prevention of metastatic spread from primary tumors