Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

Nucleation rates in flat and curved space

Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we consider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperature in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls, and monopoles during inflation. The instantons for these processes are spherical world sheets or world lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical world sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results reproduce those that can be obtained using second quantization methods, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.

Pair production by and electric field in (1+1)-dimensional de Sitter space

We use the method of Bogolubov transformations to compute the rate of pair production by an electric field in (1+1)-dimensional de Sitter space. The results are in agreement with those obtained previously using the instanton methods. This is true even when the size of the instanton is comparable to the size of the de Sitter horizon.

Heat kernels and thermodynamics in Rindler space

We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must compute the heat kernel in a geometry with different topology (without a conical singularity). This is done in two ways, which are shown to agree with computations performed by other methods. Also, we discuss the ambiguities in the regularization procedure and their physical consequences.

Singularity-free space-time

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity theorems are not satisfied is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.

How to measure cortical folding from MR images: a step-by-step tutorial to compute local gyrification index.

Cortical folding (gyrification) is determined during the first months of life, so that adverse events occurring during this period leave traces that will be identifiable at any age. As recently reviewed by Mangin and colleagues(2), several methods exist to quantify different characteristics of gyrification. For instance, sulcal morphometry can be used to measure shape descriptors such as the depth, length or indices of inter-hemispheric asymmetry(3). These geometrical properties have the advantage of being easy to interpret. However, sulcal morphometry tightly relies on the accurate identification of a given set of sulci and hence provides a fragmented description of gyrification. A more fine-grained quantification of gyrification can be achieved with curvature-based measurements, where smoothed absolute mean curvature is typically computed at thousands of points over the cortical surface(4). The curvature is however not straightforward to comprehend, as it remains unclear if there is any direct relationship between the curvedness and a biologically meaningful correlate such as cortical volume or surface. To address the diverse issues raised by the measurement of cortical folding, we previously developed an algorithm to quantify local gyrification with an exquisite spatial resolution and of simple interpretation. Our method is inspired of the Gyrification Index(5), a method originally used in comparative neuroanatomy to evaluate the cortical folding differences across species. In our implementation, which we name local Gyrification Index (lGI(1)), we measure the amount of cortex buried within the sulcal folds as compared with the amount of visible cortex in circular regions of interest. Given that the cortex grows primarily through radial expansion(6), our method was specifically designed to identify early defects of cortical development. In this article, we detail the computation of local Gyrification Index, which is now freely distributed as a part of the FreeSurfer Software (http://surfer.nmr.mgh.harvard.edu/, Martinos Center for Biomedical Imaging, Massachusetts General Hospital). FreeSurfer provides a set of automated reconstruction tools of the brain's cortical surface from structural MRI data. The cortical surface extracted in the native space of the images with sub-millimeter accuracy is then further used for the creation of an outer surface, which will serve as a basis for the lGI calculation. A circular region of interest is then delineated on the outer surface, and its corresponding region of interest on the cortical surface is identified using a matching algorithm as described in our validation study(1). This process is repeatedly iterated with largely overlapping regions of interest, resulting in cortical maps of gyrification for subsequent statistical comparisons (Fig. 1). Of note, another measurement of local gyrification with a similar inspiration was proposed by Toro and colleagues(7), where the folding index at each point is computed as the ratio of the cortical area contained in a sphere divided by the area of a disc with the same radius. The two implementations differ in that the one by Toro et al. is based on Euclidian distances and thus considers discontinuous patches of cortical area, whereas ours uses a strict geodesic algorithm and include only the continuous patch of cortical area opening at the brain surface in a circular region of interest.

Partition coefficient and molecular flexibility: the concept of lipophilicity space.

The rationale of this study was to investigate molecular flexibility and its influence on physicochemical properties with a view to uncovering additional information on the fuzzy concept of dynamic molecular structure. Indeed, it is now known that computed molecular interaction fields (MIFs) such as molecular electrostatic potentials (MEPs) and lipophilicity potentials (MLPs) are conformation-dependent, as are dipole moments. A database of 125 compounds was used whose conformational space was explored, while conformation-dependent parameters were computed for each non-redundant conformer found in the conformational space of the compounds. These parameters were the virtual log P (log P(MLP), calculated by a MLP approach), the apolar surface area (ASA), polar surface area (PSA), and solvent-accessible surface (SAS). For each compound, the range taken by each parameter (its property space) was divided by the number of rotors taken as an index of flexibility, yielding a parameter termed 'molecular sensitivity'. This parameter was poorly correlated with others (i.e., it contains novel information) and showed the compounds to fall into two broad classes. 'Sensitive' molecules are those whose computed property ranges are markedly sensitive to conformational effects, whereas 'insensitive' (in fact, less sensitive) molecules have property ranges which are comparatively less affected by conformational fluctuations. A pharmacokinetic application is presented.

Shift in cytotype frequency and niche space in the invasive plant Centaurea maculosa.

Polyploidy is often assumed to increase the spread and thus the success of alien plant species, but few empirical studies exist. We tested this hypothesis with Centaurea maculosa Lam., a species native to Europe and introduced into North America approximately 120 years ago where it became highly invasive. We analyzed the ploidy level of more than 2000 plants from 93 native and 48 invasive C. maculosa populations and found a pronounced shift in the relative frequency of diploid and tetraploid cytotypes. In Europe diploid populations occur in higher frequencies than tetraploids and only four populations had both cytotypes, while in North America diploid plants were found in only one mixed population and thus tetraploids clearly dominated. Our results showed a pronounced shift in the climatic niche between tetraploid populations in the native and introduced range toward drier climate in North America and a similar albeit smaller shift between diploids and tetraploids in the native range. The field data indicate that diploids have a predominately monocarpic life cycle, while tetraploids are often polycarpic. Additionally, the polycarpic life-form seems to be more prevalent among tetraploids in the introduced range than among tetraploids in the native range. Our study suggests that both ploidy types of C. maculosa were introduced into North America, but tetraploids became the dominant cytotype with invasion. We suggest that the invasive success of C. maculosa is partly due to preadaptation of the tetraploid cytotype in Europe to drier climate and possibly further adaptation to these conditions in the introduced range. The potential for earlier and longer seed production associated with the polycarpic life cycle constitutes an additional factor that may have led to the dominance of tetraploids over diploids in the introduced range.