GP-SUM. Gaussian Processes Filtering of non-Gaussian Beliefs

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attribute of GP-SUM is that it does not rely on linearizations of the dynamic or observation models, or on unimodal Gaussian approximations of the belief, hence enables tracking complex state distributions. The algorithm can be seen as a combination of a sampling-based filter with a probabilistic Bayes filter. On the one hand, GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. On the other hand, it achieves effective sampling and accurate probabilistic propagation by relying on the GP form of the system, and the sum-of-Gaussian form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also demonstrate its use in a pushing task, predicting with experimental accuracy the naturally occurring non-Gaussian distributions.Comment: WAFR 2018, 16 pages, 7 figure

Macro-microcirculation in the lower extremities - possible relationship

Impaired blood supply is a significant risk factor for diabetic foot ulceration and gangrene. A possible relationship between peripheral macroangiopathy and the spectral components of microvascular skin blood flow in the lower extremities was tested in diabetic patients (DP) and non-diabetic subjects (C). Basal skin blood flow (BSBF) was recorded for 30 min at the right and left medial malleolus (predominantly nutritive capillary circulation) by laser Doppler flowmetry in 64 DP and 31 C. Its oscillatory components were analyzed using wavelet transform. Peripheral arterial obliterative disease (PAOD) was defined according to ankle/brachial index (ABI): PAOD+ (ABI < 0.9: 21 DP, 12 C), PAOD− (ABI 0.91–1.3: 43 DP, 19 C). No statistically significant differences in BSBF and its oscillatory components were observed between PAOD+ and PAOD−, neither in DP nor in C. In DP, the spectral component of microvascular flow associated with endothelial activity was in significant positive correlation with systolic pressures on brachial and dorsal pedal artery (p = 0.001 and 0.010, respectively). These results indicate that mean BSBF and its oscillatory components do not change with diabetic PAOD; however there is a strong correlation between systolic pressure and the oscillatory components of BSBF related to endothelial activity manifested in the frequency interval 0.0095–0.02 Hz

Formaldehyde oxime - nitrosomethane tautomerism

Formaldehyde oxime ⇌ nitrosomethane tautomerism, isomeric nitrone, and their common cations and anions are studied with Gaussian-2 theory using MP2(full)/6-31G* geometries and with density functional theory using B3LYP/6-311+G**. Geometrical parameters, harmonic vibrational frequencies, relative stabilities, conformational stabilities, and ionization energies are compared with experimental gas-phase data when available. The formaldehyde oxime ⇌ nitrosomethane tautomerism is compared with the amide ⇌ imidol, imine ⇌ enamine, keto ⇌ enol, and nitro ⇌ aci-nitro tautomeric processes. Solvent effects are estimated by the self-consistent isodensity polarizable continuum model (SCIPCM). The influence of hydrogen bonding interactions with the solvent is addressed by including two water molecules. In the final evaluation, formaldehyde oxime is 15.8 kcal/mol more stable than nitrosomethane when the aqueous solvation correction of 3.8 kcal/mol is applied to the G2 energies. Unsolvated formaldehyde oxime is estimated to be 11.1 kcal/mol more stable than nitrone. The estimated gas-phase ionization energies (G2) are 362.5 kcal/mol for formaldehyde oxime, 350.6 kcal/mol for nitrosomethane, and 351.4 kcal/mol for nitrone

Skin Blood Flow in the Upper and Lower Extremities of Diabetic Patients with and without Autonomic Neuropathy

Background: Microvascular blood flow in the human skin is subject to rhythmic variations reflecting the influence of heartbeat, respiration, intrinsic myogenic activity, neurogenic factors and endothelial activity. The aim of our study was to test the hypothesis that basal skin blood flow (BSBF) and its dynamic components differ (1) among diabetic patients without autonomic neuropathy and with it and healthy control subjects, and (2) among the upper and lower extremities. Patients and Methods: BSBF at four recording sites with predominantly nutritive capillary circulation (right and left caput ulnae, right and left medial malleolus) was measured by laser Doppler flowmetry in 25 diabetic patients without cardiovascular autonomic neuropathy (D), 18 neuropathic diabetic patients (DAN) and 36 healthy controls (C). Wavelet transform was applied to the laser Doppler signal. Results: In absolute terms, mean flow, mean amplitude of the total spectrum and mean amplitudes at all frequency intervals were highest in C, followed by DAN and lowest in D. However, these differences were statistically significant only in the left arm. Within all three groups, mean flow and spectral amplitudes were significantly higher in the arms than in the legs, besides there was a significant difference between the two arms in D. Conclusion: We have confirmed the differences in BSBF among D, DAN and C, and demonstrated differences among the four recording sites which have not been previously described. The latter indicates an uneven progression of autonomic neuropathy and allows for speculation that the left arm is the latest to be affected