Probabilistic Invariant Learning with Randomized Linear Classifiers

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage randomness and design models that are both expressive and invariant but use less resources. Inspired by randomized algorithms, our key insight is that accepting probabilistic notions of universal approximation and invariance can reduce our resource requirements. More specifically, we propose a class of binary classification models called Randomized Linear Classifiers (RLCs). We give parameter and sample size conditions in which RLCs can, with high probability, approximate any (smooth) function while preserving invariance to compact group transformations. Leveraging this result, we design three RLCs that are provably probabilistic invariant for classification tasks over sets, graphs, and spherical data. We show how these models can achieve probabilistic invariance and universality using less resources than (deterministic) neural networks and their invariant counterparts. Finally, we empirically demonstrate the benefits of this new class of models on invariant tasks where deterministic invariant neural networks are known to struggle

High Precision Orientation Mapping from 4D-STEM Precession Electron Diffraction data through Quantitative Analysis of Diffracted Intensities

The association of scanning transmission electron microscopy (STEM) and the detection of a diffraction pattern at each probe position (so-called 4D-STEM) represents one of the most promising approaches to analyze structural properties of materials with nanometric resolution and low irradiation levels. This is widely used for texture analysis of material using automated crystal orientation mapping (ACOM). Herein, we perform orientation mapping in InP nanowires exploiting precession electron diffraction (PED) patterns acquired by an axial CMOS camera. Crystal orientation is determined at each probe position by the quantitative analysis of diffracted intensities minimizing a residue comparing experiments and simulations in analogy to structural refinement. Our simulations are based on the two-beam dynamical diffraction approximation and yield a high angular precision (~0.03 degrees), much lower than the traditional ACOM based on pattern matching algorithms (~1 degrees). We anticipate that simultaneous exploration of both spot positions and high precision crystal misorientation will allow the exploration of the whole potentiality provided by PED-based 4D-STEM for the characterization of deformation fields in nanomaterials.Comment: 31 pages, 6 figures, 1 table and supplementary informatio

Control of Small Spacecraft by Optimal Output Regulation: A Reinforcement Learning Approach

The growing number of noncooperative flying objects has prompted interest in sample-return and space debris removal missions. Current solutions are both costly and largely dependent on specific object identification and capture methods. In this paper, a low-cost modular approach for control of a swarm flight of small satellites in rendezvous and capture missions is proposed by solving the optimal output regulation problem. By integrating the theories of tracking control, adaptive optimal control, and output regulation, the optimal control policy is designed as a feedback-feedforward controller to guarantee the asymptotic tracking of a class of reference input generated by the leader. The estimated state vector of the space object of interest and communication within satellites is assumed to be available. The controller rejects the nonvanishing disturbances injected into the follower satellite while maintaining the closed-loop stability of the overall leader-follower system. The simulation results under the Basilisk-ROS2 framework environment for high-fidelity space applications with accurate spacecraft dynamics, are compared with those from a classical linear quadratic regulator controller, and the results reveal the efficiency and practicality of the proposed method

THE INFLUENCE OF HIV-1 SUBTYPES C, CRF31_BC AND B ON DISEASE PROGRESSION AND INITIAL VIROLOGIC RESPONSE TO HAART IN A SOUTHERN BRAZILIAN COHORT

Background: Although most HIV-1 infections in Brazil are due to subtype B, Southern Brazil has a high prevalence of subtype C and recombinant forms, such as CRF31_BC. This study assessed the impact of viral diversity on clinical progression in a cohort of newly diagnosed HIV-positive patients. Methods: From July/2004 to December/2005, 135 HIV-infected patients were recruited. The partial pol region was subtyped by phylogeny. A generalized estimating equation (GEE) model was used to examine the relationship between viral subtype, CD4+ T cell count and viral load levels before antiretroviral therapy. Hazard ratio (Cox regression) was used to evaluate factors associated with viral suppression (viral load < 50 copies/mL at six months). Results: Main HIV-1 subtypes included B (29.4%), C (28.2%), and CRF31_BC (23.5%). Subtypes B and C showed a similar trend in CD4+ T cell decline. Comparison of non-B (C and CRF31_BC) and B subtypes revealed no significant difference in the proportion of patients with viral suppression at six months (week 24). Higher CD4+ T cell count and lower viral load were independently associated with viral suppression. Conclusion: No significant differences were found between subtypes; however, lower viral load and higher CD4+ T cell count before therapy were associated with better response.Introdução: Embora a maioria das infecções de HIV-1 no Brasil seja devido ao subtipo B, o Sul do Brasil apresenta uma alta prevalência do subtipo C e formas recombinantes, como CRF31_BC. Este estudo avaliou o impacto da diversidade viral na evolução clínica em uma coorte de pacientes HIV-positivos recém diagnosticados. Métodos: De julho/2004 a dezembro/2005, 135 pacientes anti-HIV reagentes foram recrutados. A região pol parcial foi subtipada por filogenia. Um modelo de equação de estimativa generalizada (GEE) foi utilizado para examinar a relação entre subtipo viral, contagem de células CD4 e níveis de carga viral pré-terapia antirretroviral. Hazard ratio (regressão de Cox) foi utilizada para avaliar os fatores associados à supressão viral (carga viral < 50 cópias/mL em seis meses). Resultados: Os principais subtipos de HIV-1 incluíram B (29,4%), C (28,2%) e CRF31_BC (23,5%). Os subtipos B e C apresentaram uma tendência semelhante no declínio de células CD4. Quando comparados os subtipos não B (C e CRF31_BC) e B, não houve diferença significativa na proporção de pacientes com supressão viral aos seis meses (24 semanas). CD4 mais alto e carga viral mais baixa demonstraram associação independente com supressão viral. Conclusão: Não houve diferença significativa entre os subtipos; entretanto, viremia mais baixa e CD4 mais alto pré-terapia mostraram associação com melhor resposta

Reviewing the History of HIV-1: Spread of Subtype B in the Americas

The dispersal of HIV-1 subtype B (HIV-1B) is a reflection of the movement of human populations in response to social, political, and geographical issues. The initial dissemination of HIV-1B outside Africa seems to have included the passive involvement of human populations from the Caribbean in spreading the virus to the United States. However, the exact pathways taken during the establishment of the pandemic in the Americas remain unclear. Here, we propose a geographical scenario for the dissemination of HIV-1B in the Americas, based on phylogenetic and genetic statistical analyses of 313 available sequences of the pol gene from 27 countries. Maximum likelihood and Bayesian inference methods were used to explore the phylogenetic relationships between HIV-1B sequences, and molecular variance estimates were analyzed to infer the genetic structure of the viral population. We found that the initial dissemination and subsequent spread of subtype B in the Americas occurred via a single introduction event in the Caribbean around 1964 (1950–1967). Phylogenetic trees present evidence of several primary outbreaks in countries in South America, directly seeded by the Caribbean epidemic. Cuba is an exception insofar as its epidemic seems to have been introduced from South America. One clade comprising isolates from different countries emerged in the most-derived branches, reflecting the intense circulation of the virus throughout the American continents. Statistical analysis supports the genetic compartmentalization of the virus among the Americas, with a close relationship between the South American and Caribbean epidemics. These findings reflect the complex establishment of the HIV-1B pandemic and contribute to our understanding between the migration process of human populations and virus diffusion

THE INFLUENCE OF HIV-1 SUBTYPES C, CRF31_BC AND B ON DISEASE PROGRESSION AND INITIAL VIROLOGIC RESPONSE TO HAART IN A SOUTHERN BRAZILIAN COHORT

Background: Although most HIV-1 infections in Brazil are due to subtype B, Southern Brazil has a high prevalence of subtype C and recombinant forms, such as CRF31_BC. This study assessed the impact of viral diversity on clinical progression in a cohort of newly diagnosed HIV-positive patients. Methods: From July/2004 to December/2005, 135 HIV-infected patients were recruited. The partial pol region was subtyped by phylogeny. A generalized estimating equation (GEE) model was used to examine the relationship between viral subtype, CD4+ T cell count and viral load levels before antiretroviral therapy. Hazard ratio (Cox regression) was used to evaluate factors associated with viral suppression (viral load < 50 copies/mL at six months). Results: Main HIV-1 subtypes included B (29.4%), C (28.2%), and CRF31_BC (23.5%). Subtypes B and C showed a similar trend in CD4+ T cell decline. Comparison of non-B (C and CRF31_BC) and B subtypes revealed no significant difference in the proportion of patients with viral suppression at six months (week 24). Higher CD4+ T cell count and lower viral load were independently associated with viral suppression. Conclusion: No significant differences were found between subtypes; however, lower viral load and higher CD4+ T cell count before therapy were associated with better response