Unification modulo a partial theory of exponentiation

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Computer aided Design and Optimization of Mineral Processing Plants by a State of the Art Simulator

Tata Research Development and Design Centre (TRDDC) has developed a state of the art mineral processing simulator called SimL8. It performs modelling, simulation and optimisation functions and provides viable strategies for enhancement of the performance of mineral processing plants. A number of case studies on plant diagnostics, grinding,classification, flotation and pressure filtration are taken up to demonstrate the utility of modelling and simulation on SimL8 platform

Information entropy and nucleon correlations in nuclei

The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator model and with the short-range correlated distributions. It is found that $S_r$ depends strongly on $\ln A$ and does not depend very much on the model. The behaviour of $S_k$ is opposite. The various cases we consider can be classified according to either the quantity of the experimental data we use or by the values of $S$, i.e., the increase of the quality of the density and of the momentum distributions leads to an increase of the values of $S$. In all cases, apart from the linear relation $S=a+b\ln A$, the linear relation $S=a_V+b_V \ln V$ also holds. V is the mean volume of the nucleus. If $S$ is considered as an ensemble entropy, a relation between $A$ or $V$ and the ensemble volume can be found. Finally, comparing different electron scattering experiments for the same nucleus, it is found that the larger the momentum transfer ranges, the larger the information entropy is. It is concluded that $S$ could be used to compare different experiments for the same nucleus and to choose the most reliable one.Comment: 14 pages, 4 figures, 2 table

White matter integrity as a predictor of response to treatment in first episode psychosis

The integrity of brain white matter connections is central to a patient's ability to respond to pharmacological interventions. This study tested this hypothesis using a specific measure of white matter integrity, and examining its relationship to treatment response using a prospective design in patients within their first episode of psychosis. Diffusion tensor imaging data were acquired in 63 patients with first episode psychosis and 52 healthy control subjects (baseline). Response was assessed after 12 weeks and patients were classified as responders or non-responders according to treatment outcome. At this second time-point, they also underwent a second diffusion tensor imaging scan. Tract-based spatial statistics were used to assess fractional anisotropy as a marker of white matter integrity. At baseline, non-responders showed lower fractional anisotropy than both responders and healthy control subjects (P < 0.05; family-wise error-corrected), mainly in the uncinate, cingulum and corpus callosum, whereas responders were indistinguishable from healthy control subjects. After 12 weeks, there was an increase in fractional anisotropy in both responders and non-responders, positively correlated with antipsychotic exposure. This represents one of the largest, controlled investigations of white matter integrity and response to antipsychotic treatment early in psychosis. These data, together with earlier findings on cortical grey matter, suggest that grey and white matter integrity at the start of treatment is an important moderator of response to antipsychotics. These findings can inform patient stratification to anticipate care needs, and raise the possibility that antipsychotics may restore white matter integrity as part of the therapeutic response

A high-order Nystrom discretization scheme for boundary integral equations defined on rotationally symmetric surfaces

A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e.g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting recursion relations for Legendre functions. Numerical examples illustrate the performance of the scheme; in particular, it is demonstrated that for a BIE associated with Laplace's equation on a surface discretized using 320,800 points, the set-up phase of the algorithm takes 1 minute on a standard laptop, and then solves can be executed in 0.5 seconds.Comment: arXiv admin note: substantial text overlap with arXiv:1012.56301002.200

The detection, treatment, and biology of epithelial ovarian cancer

Ovarian cancer is particularly insidious in nature. Its ability to go undetected until late stages coupled with its non-descript signs and symptoms make it the seventh leading cause of cancer related deaths in women. Additionally, the lack of sensitive diagnostic tools and resistance to widely accepted chemotherapy regimens make ovarian cancer devastating to patients and families and frustrating to medical practitioners and researchers. Here, we provide an in-depth review of the theories describing the origin of ovarian cancer, molecular factors that influence its growth and development, and standard methods for detection and treatment. Special emphasis is focused on interactions between ovarian tumors and the innate and adaptive immune system and attempts that are currently underway to devise novel immunotherapeutic approaches for the treatment of ovarian tumors

Gall Bladder And Common Bile Duct Stones – When Is Direct Cholangiography Indicated?

The medical records of 277 consecutive patients who underwent cholecystectomy for benign gall stone disease, were reviewed to determine the incidence and cause of biliary tract obstructuion

Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

Magnetic properties of copper amalgams

Magnetic properties of dilute as well as concentrated amalgams have been investigated. It has been shown that when dilute amalgams are prepared by prolonged electrolysis at room temperature the diamagnetic susceptibilty of the amalgams prepared is lower than that calculated on the mixture law and the results are in line with those of Venkataramiah; but if the amalgams are prepared at low temperature, 0° C., within 4-5 hours or by grinding the components according to the method of Terry and Wright susceptibility value of the amalgams obeys the mixture law. This difference in the susceptibility has been explained by the authors, by suggesting the formation of paragmanetic oxides formed during prolonged electrolysis at high temperatures. Amalgams of higher concentrations prepared by grinding method, when fresh obey the mixture law but on keeping, even under vacuum, become less diamagnetic and the maximum difference, in susceptibility values between a fresh and an aged amalgam is observed in one which contains 34 per cent. copper. This is supposed to be due to the formation of compound

Striatal vs extrastriatal dopamine D2 receptors in antipsychotic response - a double-blind PET study in schizophrenia

Blockade of dopamine D2 receptors remains a common feature of all antipsychotics. It has been hypothesized that the extrastriatal (cortical, thalamic) dopamine D2 receptors may be more critical to antipsychotic response than the striatal dopamine D2 receptors. This is the first double-blind controlled study to examine the relationship between striatal and extrastriatal D2 occupancy and clinical effects. Fourteen patients with recent onset psychosis were assigned to low or high doses of risperidone (1 mg vs 4 mg/day) or olanzapine (2.5 mg vs 15 mg/day) in order to achieve a broad range of D2 occupancy levels across subjects. Clinical response, side effects, striatal ([11C]-raclopride-positron emission tomography (PET)), and extrastriatal ([11C]-FLB 457-PET) D2 receptors were evaluated after treatment. The measured D2 occupancies ranged from 50 to 92% in striatal and 4 to 95% in the different extrastriatal (frontal, temporal, thalamic) regions. Striatal and extrastriatal occupancies were correlated with dose, drug plasma levels, and with each other. Striatal D2 occupancy predicted response in positive psychotic symptoms (r=0.62, p=0.01), but not for negative symptoms (r=0.2, p=0.5). Extrastriatal D2 occupancy did not predict response in positive or negative symptoms. The two subjects who experienced motor side effects had the highest striatal occupancies in the cohort. Striatal D2 blockade predicted antipsychotic response better than frontal, temporal, and thalamic occupancy. These results, when combined with the preclinical data implicating the mesolimbic striatum in antipsychotic response, suggest that dopamine D2 blockade within specific regions of the striatum may be most critical for ameliorating psychosis in schizophrenia.peer-reviewe