QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexponential algorithm running in time 2^{O~(n^{2/3})} for Maximum Clique on disk graphs. In stark contrast, Maximum Clique on intersection graphs of filled ellipses or filled triangles is unlikely to have such algorithms, even when the ellipses are close to unit disks. Indeed, we show that there is a constant ratio of approximation which cannot be attained even in time 2^{n^{1-epsilon}}, unless the Exponential Time Hypothesis fails

Magnetic properties of σ\sigma-FeCr alloy as calculated with the charge and spin self-consistent KKR(CPA) method

Magnetic properties of a $\sigma-$Fe$_{16}$Cr$_{14}$ alloy calculated with the charge and spin self- consistent Korringa-Kohn-Rostoker (KKR) and combined with coherent potential approximation (KKR-CPA) methods are reported. Non-magnetic state as well as various magnetic orderings were considered, i.e. ferromagnetic (FM) and more complex anti-parallel (called APM) arrangements for selected sublattices, as follows from the symmetry analysis. It has been shown that the Stoner criterion applied to non-magnetic density of states at the Fermi energy, $E_F$ is satisfied for Fe atoms situated on all five lattice sites, while it is not fulfilled for all Cr atoms. In FM and APM states, the values of magnetic moments on Fe atoms occupying various sites are dispersed between 0 and 2.5 $\mu_B$, and they are proportional to the number of Fe atoms in the nearest-neighbor shell. Magnetic moments of Cr atoms havin much smaller values were found to be coupled antiparallel to those of Fe atoms. The average value of the magnetic moment per atom was found to be $=0.55 \mu_B$ that is by a factor of 4 larger than the experimental value found for a $\sigma-$Fe$_{0.538}$Cr$_{0.462}$ sample. Conversely, admitting an anti- parallel ordering (APM model) on atoms situated on C and D sites, according to the group theory and symmetry analysis results, yielded a substantial reduction of to 0.20 $\mu_B$. Further diminution of to 0.15 $\mu_B$, which is very close to the experimental value of 0.14 $\mu_B$, has been achieved with the KKR-CPA calculations by considering a chemical disorder on sites B, C and D

Measurement of Electron Trapping in the CESR Storage Ring

The buildup of low-energy electrons has been shown to affect the performance of a wide variety of particle accelerators. Of particular concern is the persistence of the cloud between beam bunch passages, which can impose limitations on the stability of operation at high beam current. We have obtained measurements of long-lived electron clouds trapped in the field of a quadrupole magnet in a positron storage ring, with lifetimes much longer than the revolution period. Based on modeling, we estimate that about 7% of the electrons in the cloud generated by a 20-bunch train of 5.3 GeV positrons with 16-ns spacing and $1.3x10^{11}$ population survive longer than 2.3 $\mu$s in a quadrupole field of gradient 7.4 T/m. We have observed a non-monotonic dependence of the trapping effect on the bunch spacing. The effect of a witness bunch on the measured signal provides direct evidence for the existence of trapped electrons. The witness bunch is also observed to clear the cloud, demonstrating its effectiveness as a mitigation technique.Comment: 6 pages, 9 figures, 28 citation

Small Scale Temporal and Spatial Variability of Potassium Soil Test Values On A Crider Soil

An on-farm, small plot study conducted in 1996, on a Crider soil in Larue County, Kentucky, resulted in unanticipated wide variability of soil test potassium (STK) values between spring and fall sampling. Because of this, the small plots were sampled monthly over a period of time with the objective of determining if such variability in STK values was real

Riesz transform characterization of Hardy spaces associated with Schr\"odinger operators with compactly supported potentials

Let L=-\Delta+V be a Schr\"odinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\in H_L^1 if and only if R_j f \in L^1(R^d) for j=1,...,d, where R_j= \frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L.Comment: 6 page

Three-dimensional topological lattice models with surface anyons

We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they may well capture the topological behavior of some strongly correlated systems. In this work we give a full pedagogical treatment of a special simple case of these models, which we call the 3D semion model: We calculate its ground state degeneracies for a variety of boundary conditions, and classify its low-lying excitations. While point defects in the bulk are confined in pairs connected by energetic strings, the surface excitations are more interesting: the model has deconfined point defects pinned to the boundary of the lattice, and these exhibit semionic braiding statistics. The surface physics is reminiscent of a $\nu=1/2$ bosonic fractional quantum Hall effect in its topological limit, and these considerations help motivate an effective field theoretic description for the lattice models as variants of $bF$ theories. Our special example of the 3D semion model captures much of the behavior of more general `confined Walker-Wang models'. We contrast the 3D semion model with the closely related 3D version of the toric code (a lattice gauge theory) which has deconfined point excitations in the bulk and we discuss how more general models may have some confined and some deconfined excitations. Having seen that there exist lattice models whose surfaces have the same topological order as a bosonic fractional quantum Hall effect on a confining bulk, we construct a lattice model whose surface has similar topological order to a fermionic quantum hall effect. We find that in these models a fermion is always deconfined in the three dimensional bulk

Relationship between interoceptive sensibility and somatoform disorders in adults with autism spectrum traits. The mediating role of alexithymia and emotional dysregulation

OBJECTIVE: The purpose of the study is to analyses the relationship between interoceptive sensibility and somatoform disorders among persons with Autism Spectrum Disorder (ASD). It has been assumed that the interoceptive sensibility is accompanied by a high level of alexithymia and emotion dysregulation in somatoform disorders. METHODS: Persons under the care of the foundation helping people with ASD were asked to participate in the study. In total, 205 people took part in the research. The participants aged from 18 to 63 (M = 34.91; SD = 8.44). The ASD group comprised 79 persons (38.5% of subjects). The control group comprised 126 individuals (61.5% of subjects). Participants completed self-report questionnaires measuring autism (AQ), interoceptive sensibility (BPQ), alexithymia (TAS20), emotional dysregulation (DERS), and somatoform disorder (SDQ). RESULTS: The analyses showed a moderation effect of the group, which indicates the existence of a relationship between interoceptive sensibility and somatoform disorders to the greater extent in the clinical group than in the control group. In addition, the serial multiple mediation model analysis allowed to verify the mediating effect of emotion dysregulation and alexithymia on the abovementioned relationship. The indirect effect, which assumed the mediating role of alexithymia turned out to be significant, contrary to the indirect effect where emotion dysregulation was a mediator in a situation where both variables were applied simultaneously. CONCLUSIONS: Interoceptive sensibility correlated with level of alexithymia, in particular, difficulties in identifying and verbalizing emotions and emotion dysregulation in the lack of emotional awareness and lack of emotional clarity and is associated with somatoform disorders in the investigated group regardless of participants’ belonging to the ASD or control group

GRB 110328A/Swift J164449.3+573451: The Tidal Obliteration of a Deeply Plunging Star?

We examine the tidal disruption event scenario to explain Sw 1644+57, a powerful and persistent X-ray source which suddenly became active as GRB 110328A. The precise localization at the center of a z=0.35 galaxy argues for activity of the central engine as the underlying cause. We look at the suggestion by Bloom et al of the possibility of a tidal disruption event (TDE). We argue that Sw 1644+57 cannot be explained by the traditional TDE model in which the periastron distance is close to the tidal disruption radius - three independent lines of argument indicate the orbit must be deeply plunging or else the powerful jet we are observing could not be produced. These arguments stem from (i) comparing the early X-ray light curve to the expected theoretical fallback rate, (ii) looking at the time of transition to disk-dominated decay, and (iii) considering the TDE rate. Due to the extreme excess in the tidal force above that which would be required minimally to disrupt the star in a deeply plunging orbit at periastron, we suggest this scenario might be referred to more descriptively as a TOE (tidal obliteration event) rather than a TDE.Comment: 7 pages, 2 figures, accepted by the Astrophysical Journal, major revisions since vers. [1]; corrupted file in vers. [2] replace