Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for solution of the time dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time dependent PDEs often use finite difference for time, and a spectral scheme for the spatial dimensions, which leads to slow linear convergence. Spectral collocation space-time methods show exponential convergence, however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to very high compression of linear operators from terabytes to kilobytes in TT-format, and tens of thousands times speedup when compared to full grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions

Tensor Networks for Solving Realistic Time-independent Boltzmann Neutron Transport Equation

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial Differential Equations (PDEs). Here, we present a mixed Tensor Train (TT)/Quantized Tensor Train (QTT) approach for the numerical solution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian geometry. Discretizing a realistic three-dimensional (3D) BNTE by (i) diamond differencing, (ii) multigroup-in-energy, and (iii) discrete ordinate collocation leads to huge generalized eigenvalue problems that generally require a matrix-free approach and large computer clusters. Starting from this discretization, we construct a TT representation of the PDE fields and discrete operators, followed by a QTT representation of the TT cores and solving the tensorized generalized eigenvalue problem in a fixed-point scheme with tensor network optimization techniques. We validate our approach by applying it to two realistic examples of 3D neutron transport problems, currently solved by the PARallel TIme-dependent SN (PARTISN) solver. We demonstrate that our TT/QTT method, executed on a standard desktop computer, leads to a yottabyte compression of the memory storage, and more than 7500 times speedup with a discrepancy of less than 1e-5 when compared to the PARTISN solution.Comment: 38 pages, 9 figure

Study of the Isomeric Ratio of 135m,g 54Xe in Photofission 23793Np in Giant Dipole Resonance Region

In this work we present the results of measurement of the isomeric ratio of fission fragment e in photofission of 237Np induced by bremsstrahlung in the Giant Dipole Resonance Region by the method using the inert gaseous flow. The experiments have been performed at the electron accelerator Microtron MT-25 of the Flerov laboratory of Nuclear Reaction, Joint Institute for Nuclear Research, Dubna, Russia. The results were discussed and compared with that of other authors

Elite control of HIV is associated with distinct functional and transcriptional signatures in lymphoid tissue CD8+ T cells

The functional properties of circulating CD8+ T cells have been associated with immune control of HIV. However, viral replication occurs predominantly in secondary lymphoid tissues, such as lymph nodes (LNs). We used an integrated single-cell approach to characterize effective HIV-specific CD8+ T cell responses in the LNs of elite controllers (ECs), defined as individuals who suppress viral replication in the absence of antiretroviral therapy (ART). Higher frequencies of total memory and follicle-homing HIV-specific CD8+ T cells were detected in the LNs of ECs compared with the LNs of chronic progressors (CPs) who were not receiving ART. Moreover, HIV-specific CD8+ T cells potently suppressed viral replication without demonstrable cytolytic activity in the LNs of ECs, which harbored substantially lower amounts of CD4+ T cell–associated HIV DNA and RNA compared with the LNs of CPs. Single-cell RNA sequencing analyses further revealed a distinct transcriptional signature among HIV-specific CD8+ T cells from the LNs of ECs, typified by the down-regulation of inhibitory receptors and cytolytic molecules and the up-regulation of multiple cytokines, predicted secreted factors, and components of the protein translation machinery. Collectively, these results provide a mechanistic framework to expedite the identification of novel antiviral factors, highlighting a potential role for the localized deployment of noncytolytic functions as a determinant of immune efficacy against HIV

Social Determinants of Long Lasting Insecticidal Hammock-Use Among the Ra-Glai Ethnic Minority in Vietnam: Implications for Forest Malaria Control

BACKGROUND: Long-lasting insecticidal hammocks (LLIHs) are being evaluated as an additional malaria prevention tool in settings where standard control strategies have a limited impact. This is the case among the Ra-glai ethnic minority communities of Ninh Thuan, one of the forested and mountainous provinces of Central Vietnam where malaria morbidity persist due to the sylvatic nature of the main malaria vector An. dirus and the dependence of the population on the forest for subsistence - as is the case for many impoverished ethnic minorities in Southeast Asia. METHODS: A social science study was carried out ancillary to a community-based cluster randomized trial on the effectiveness of LLIHs to control forest malaria. The social science research strategy consisted of a mixed methods study triangulating qualitative data from focused ethnography and quantitative data collected during a malariometric cross-sectional survey on a random sample of 2,045 study participants. RESULTS: To meet work requirements during the labor intensive malaria transmission and rainy season, Ra-glai slash and burn farmers combine living in government supported villages along the road with a second home at their fields located in the forest. LLIH use was evaluated in both locations. During daytime, LLIH use at village level was reported by 69.3% of all respondents, and in forest fields this was 73.2%. In the evening, 54.1% used the LLIHs in the villages, while at the fields this was 20.7%. At night, LLIH use was minimal, regardless of the location (village 4.4%; forest 6.4%). DISCUSSION: Despite the free distribution of insecticide-treated nets (ITNs) and LLIHs, around half the local population remains largely unprotected when sleeping in their forest plot huts. In order to tackle forest malaria more effectively, control policies should explicitly target forest fields where ethnic minority farmers are more vulnerable to malaria