Lie point symmetries and the geodesic approximation for the Schr\"odinger-Newton equations

We consider two problems arising in the study of the Schr\"odinger-Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to widely separated lumps of probability. The lumps are found to move like point particles under a mutual inverse-square law of attraction

Cosmic bulk viscosity through backreaction

We consider an effective viscous pressure as the result of a backreaction of inhomogeneities within Buchert's formalism. The use of an effective metric with a time-dependent curvature radius allows us to calculate the luminosity distance of the backreaction model. This quantity is different from its counterpart for a "conventional" spatially flat bulk viscous fluid universe. Both expressions are tested against the SNIa data of the Union2.1 sample with only marginally different results for the distance-redshift relation and in accordance with the $\Lambda$CDM model. Future observations are expected to be able to discriminate among these models on the basis of indirect measurements of the curvature evolution.Comment: 18 pages, 6 figures, comments and references added, accepted for publication in GR

An improved sum-product estimate for general finite fields

This paper improves on a sum-product estimate obtained by Katz and Shen for subsets of a finite field whose order is not prime

Long-term variation in the Sun's activity caused by magnetic Rossby waves in the tachocline

Long-term records of sunspot number and concentrations of cosmogenic radionuclides (10Be and 14C) on the Earth reveal the variation of the Sun's magnetic activity over hundreds and thousands of years. We identify several clear periods in sunspot, 10Be, and 14C data as 1000, 500, 350, 200 and 100 years. We found that the periods of the first five spherical harmonics of the slow magnetic Rossby mode in the presence of a steady toroidal magnetic field of 1200-1300 G in the lower tachocline are in perfect agreement with the time scales of observed variations. The steady toroidal magnetic field can be generated in the lower tachocline either due to the steady dynamo magnetic field for low magnetic diffusivity or due to the action of the latitudinal differential rotation on the weak poloidal primordial magnetic field, which penetrates from the radiative interior. The slow magnetic Rossby waves lead to variations of the steady toroidal magnetic field in the lower tachocline, which modulate the dynamo magnetic field and consequently the solar cycle strength. This result constitutes a key point for long-term prediction of the cycle strength. According to our model, the next deep minimum in solar activity is expected during the first half of this century.Comment: 4 pages, 4 figures, accepted in ApJ

Design, synthesis, and biological evaluation of an allosteric inhibitor of HSET that targets cancer cells with supernumerary centrosomes

Centrosomes associate with spindle poles; thus, the presence of two centrosomes promotes bipolar spindle assembly in normal cells. Cancer cells often contain supernumerary centrosomes, and to avoid multipolar mitosis and cell death, these are clustered into two poles by the microtubule motor protein HSET. We report the discovery of an allosteric inhibitor of HSET, CW069, which we designed using a methodology on an interface of chemistry and biology. Using this approach, we explored millions of compounds in silico and utilized convergent syntheses. Only compound CW069 showed marked activity against HSET in vitro. The inhibitor induced multipolar mitoses only in cells containing supernumerary centrosomes. CW069 therefore constitutes a valuable tool for probing HSET function and, by reducing the growth of cells containing supernumerary centrosomes, paves the way for new cancer therapeutics