Separating OR, SUM, and XOR Circuits.

Given a boolean n × n matrix A we consider arithmetic circuits for computing the transformation x ↦ Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on separating OR-circuits from the two other models in terms of circuit complexity: We show how to obtain matrices that admit OR-circuits of size O(n), but require SUM-circuits of size Ω(n3/2/log2n).We consider the task of rewriting a given OR-circuit as a XOR-circuit and prove that any subquadratic-time algorithm for this task violates the strong exponential time hypothesis.

Mixture model clustering of phenotype features reveals evidence for association of DTNBP1 to a specific subtype of schizophrenia.

BACKGROUND: While DTNBP1, DISC1, and NRG1 have been extensively studied as candidate genes of schizophrenia, results remain inconclusive. Possible explanations for this are that the genes might be relevant only to certain subtypes of the disease and/or only in certain populations. METHODS: We performed unsupervised clustering of individuals from Finnish schizophrenia families, based on extensive clinical and neuropsychological data, including Structured Clinical Interview for DSM-IV (SCID) information. Families with at least one affected member with DSM-IV diagnosis of a schizophrenia spectrum psychosis were included in a register-based ascertainment. Final sample consisted of 904 individuals from 288 families. We then used the cluster phenotypes in a genetic association study of candidate genes. RESULTS: A robust three-class clustering of individuals emerged: 1) psychotic disorder with mood symptoms (n = 172), 2) core schizophrenia (n = 223), and 3) absence of psychotic disorder (n = 509). One third of the individuals diagnosed with schizophrenia were assigned to cluster 1. These individuals had fewer negative and positive psychotic symptoms and cognitive deficits but more depressive symptoms than individuals in cluster 2. There was a significant association of cluster 2 cases with the DTNBP1 gene, while the DISC1 gene indicated a significant association with schizophrenia spectrum disorders based on the DSM-IV criteria. CONCLUSIONS: In the Finnish population, DTNBP1 gene is associated with a schizophrenia phenotype characterized by prominent negative symptoms, generalized cognitive impairment, and few mood symptoms. Identification of genes and pathways related to schizophrenia necessitates novel definitions of disease phenotypes associated more directly with underlying biology.

Depth profiling of compression-induced disorders and polymorphic transition on tablet surfaces with grazing incidence X-ray diffraction.

PURPOSE: The importance of induced crystal disorders like crystallite size, crystal defects, and amorphicity with respect to the dissolution rate of the drug has been discussed in many cases. Thus, the characterization of these properties is of great importance in the pharmaceutical formulation development, although the exact correlation between disorders and dissolution rate is still unclear. The aim of this study was to analyze pharmaceutical tablets with grazing incidence X-ray diffraction, which enables the depth profiling of the crystallographic properties of the tablets. To study and clarify the potential of grazing incidence diffraction in the analysis of pharmaceutical materials, the effect of the compaction process on the surface of tablets was examined. METHODS: Carbamazepine, tolbutamide, and chlorpropamide tablets, compacted using different compression pressures, were studied using grazing incidence angle X-ray diffraction. The effects of compression on the crystallographic properties were investigated as a function of the distance from the tablet surface. RESULTS: The surfaces of the tolbutamide and chlorpropamide tablets were disordered due to the compression. The manifestation of the disorder was deduced to be due to amorphicity, small crystallite size, and amount of crystal defects. The changes were mainly on the surface and diminished strongly as a function of the distance from the surface of the tablet. Moreover, the changes were dependent on the compression pressure used. The changes on the surface of the carbamazepine tablets were also due to the compression but these changes were not clearly dependent on the depth nor the compression pressure. The partial phase transition took place in the chlorpropamide tablets due to the compression. The magnitude of the transition was not highest on the surface because amorphization and texturization also took place on the tablet surface during the compression. CONCLUSIONS: The present study proved that grazing incidence X-ray diffraction is a potential novel research tool to reveal crystallographic transformations taking place on the surfaces of the tablets induced, for example, by compression pressure.

Quantitative analysis of amorphous content of lactose using CCD-Raman spectroscopy.

A Raman spectroscopy method was developed for the quantification of the amorphous content of lactose. Both physical mixtures and spray-dried samples were used and the results were compared with the IMC determinations. Sample inhomogeneities were averaged out by collecting multiple spectra from each sample, and the total measurement time remained below 10 min due to the high sensitivity of the CCD-Raman spectrometer used in the measurements. The obtained calibration error (SEC) for the physical mixtures was 1.3% (w/w) in the 0-100% amorphous content range and was reduced to 0.2% (w/w) in the 0-10% range of more practical interest. The crystallization heat values of the spray-dried samples showed a linear correlation with the Raman quantifications in the amorphous content range of 0-80%, but saturated over the 80% concentration. This finding suggests a reference value of ca. 60 J/g for the spray-dried samples, instead of the crystallization heat of amorphous lactose (ca. 50 J/g) valid in the IMC determinations of physical mixtures.

Determination of amorphous content of lactose samples by solution calorimetry.

Earlies studies suggest that solution calorimetry can be used to determine the extent of amorphous content of drug and excipient, when the solubility and dissolution rate of the compound in the chosen solvent are reasonably high. In the present study, the use of solution calorimetry for assessment of amorphous content of a sample that is not completely dissolved in a solvent was evaluated. Physical mixtures of lactose and spray-dried lactose samples were analysed. The amorphous content of the physical mixtures and the spray-dried samples varied from 0% to 100% determined by isothermal microcalorimetry. The enthalpy of solution (delta(sol)H) was determined in water. The lactose samples were dissolved quickly in water. In addition, the enthalpy accompanied with an addition of a lactose sample in an over saturated aqueous solution (delta(sat)H) (prepared from the corresponding lactose sample) was determined. The lactose sample did not completely dissolve in the over saturated aqueous solution. An excellent correlation was observed between delta(sol)H and the amorphous content of the samples. Interestingly, there was a linear correlation also between delta(sat)H and the amorphous content of the samples. Further, a linear relationship was observed between the delta(sat)H and the delta(sol)H of the samples. Therefore, solution calorimetry may represent a rapid and simple method for determining the amorphous content also in samples that are not completely dissolved in the solvent.

Characterization of the preferred orientation of delta-mannitol crystallites in tablets.

The crystallographic texture, i.e. the preferred orientation of crystallites of delta-mannitol samples, has been experimentally determined by pole figure analysis. The pole figures were measured with an X-ray diffraction texture goniometer. It was found that already the uncompressed delta-mannitol powder sample was slightly texturized so that the (0 2 0) plane was parallel to the upper surface of the sample. The degree of preferred orientation was found to significantly increase when the powder was compressed to a tablet with the minimum (74MPa) compression pressure. Nevertheless, the direction of the texture remained parallel to the tablet surface. Maximum compression (740MPa) did not increase the degree of preferred orientation further. The compression time (0 or 60s) was not found to noticeably affect the strength or direction of the texture. The extent of the texture inside the tablet was determined with a tablet surface grinding experiment. The degree of preferred orientation was found to decrease under the surface while the orientation remained the same. The results were confirmed with orientation distribution function (ODF) calculations.