Representing Edge Flows on Graphs via Sparse Cell Complexes

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such representations is to lift the graph structure to a simplicial complex: The eigenvectors of the associated Hodge-Laplacian, respectively the incidence matrices of the corresponding simplicial complex then induce a Hodge decomposition, which can be used to represent the observed data in terms of gradient, curl, and harmonic flows. In this paper, we generalize this approach to cellular complexes and introduce the cell inference optimization problem, i.e., the problem of augmenting the observed graph by a set of cells, such that the eigenvectors of the associated Hodge Laplacian provide a sparse, interpretable representation of the observed edge flows on the graph. We show that this problem is NP-hard and introduce an efficient approximation algorithm for its solution. Experiments on real-world and synthetic data demonstrate that our algorithm outperforms current state-of-the-art methods while being computationally efficient.Comment: 9 pages, 6 figures (plus appendix). For evaluation code, see https://anonymous.4open.science/r/edge-flow-repr-cell-complexes-11C

Логіка

Зміст видання відповідає освітньо-професійній програмі бакалаврів напрямів підготовки «Право», «Філософія» та інших напрямів. Розглянуто матеріал дисципліни «Логіка», зокрема такі теми: «Основні закони формальної логіки», «Поняття», «Судження», «Умовиводи», «Доведення і спростування», «Гіпотеза і теорія». Сформульовано навчальні цілі змістових модулів дисципліни, що окреслюють компетентності, навички й уміння бакалавра гуманітарних та інших спеціальностей

Improved hole extraction selectivity of polymer solar cells by combining PEDOT:PSS with WO 3

As the device performance and stability of polymer solar cells strongly depend on the interfacial charge extraction layers, the hole transport layer (HTL) properties are crucial. Furthermore, unfavorable interactions with the electrode or the photoactive layer should be screened and prevented. Organic solar cells of conventional architecture by varying the HTL material and layer stack systematically between PEDOT:PSS and a sol–gel‐derived tungsten oxide (WO 3 ) are investigated. The impact of various HTLs in the solar cells is investigated by optical and electrical characterization. Interestingly, a triple‐layer WO 3 /PEDOT:PSS/WO 3 configuration results in the best device performance specifically compared with the use of pristine WO 3 and pristine PEDOT:PSS hole extraction layers. The triple layer also shows an increased reproducibility in the lifetime, which, combined with the improvement in the efficiency, can be the keys for expectable revenue

Spatial and temporal variability in MLT turbulence inferred from in situ and ground-based observations during the WADIS-1 sounding rocket campaign

In summer 2013 the WADIS-1 sounding rocket campaign was conducted at the Andøya Space Center (ACS) in northern Norway (69° N, 16° E). Among other things, it addressed the question of the variability in mesosphere/lower thermosphere (MLT) turbulence, both in time and space. A unique feature of the WADIS project was multi-point turbulence sounding applying different measurement techniques including rocket-borne ionization gauges, VHF MAARSY radar, and VHF EISCAT radar near Tromsø. This allowed for horizontal variability to be observed in the turbulence field in the MLT at scales from a few to 100 km. We found that the turbulence dissipation rate, ε varied in space in a wavelike manner both horizontally and in the vertical direction. This wavelike modulation reveals the same vertical wavelengths as those seen in gravity waves. We also found that the vertical mean value of radar observations of ε agrees reasonably with rocket-borne measurements. In this way defined 〈εradar〉 value reveals clear tidal modulation and results in variation by up to 2 orders of magnitude with periods of 24 h. The 〈εradar〉 value also shows 12 h and shorter (1 to a few hours) modulations resulting in one decade of variation in 〈εradar〉 magnitude. The 24 h modulation appeared to be in phase with tidal change of horizontal wind observed by SAURA-MF radar. Such wavelike and, in particular, tidal modulation of the turbulence dissipation field in the MLT region inferred from our analysis is a new finding of this work

Impacts of a sudden stratospheric warming on the mesospheric metal layers

We report measurements of atomic sodium, iron and temperature in the mesosphere and lower thermosphere (MLT) made by ground-based lidars at the ALOMAR observatory (69°N, 16°E) during a major sudden stratospheric warming (SSW) event that occurred in January 2009. The high resolution temporal observations allow the responses of the Na and Fe layers to the SSW at high northern latitudes to be investigated. A significant cooling with temperatures as low as 136 K around 90 km was observed on 22 − 23 January 2009, along with substantial depletions of the Na and Fe layers (an ~80% decrease in the column abundance with respect to the mean over the observation period). The Whole Atmosphere Community Climate Model (WACCM) incorporating the chemistry of Na, Fe, Mg and K, and nudged with reanalysis data below 60 km, captures well the timing of the SSW, although the extent of the cooling and consequently the depletion in the Na and Fe layers is slightly underestimated. The model also predicts that the perturbations to the metal layers would have been observable even at equatorial latitudes. The modelled Mg layer responds in a very similar way to Na and Fe, whereas the K layer is barely affected by the SSW because of the enhanced conversion of K+ ions to K atoms at the very low temperatures

Stapedius reflex testing shows altered small muscle function in untreated Pompe patients and improvement after enzyme replacement therapy

Introduction Pompe disease primarily affects skeletal and cardiac muscles. It is difficult to assess therapeutic efficacy of enzyme replacement therapy (ERT) using primary end points based on changes in weakness of large limb-girdle muscles, gait-endurance, and respiratory function, which all depend on variable day-to-day patient performance. In contrast, muscle improvement might be shown by assessing function of very small muscles, such as the stapedius and tensor tympani muscles. We therefore tested whether ERT benefits in Pompe patients can be shown by stapedius reflex testing before and after ERT. Results In four Pompe patients, we assessed ipsilateral stapedius reflex thresholds in the right and left ear one and two years after patients received first dosage of biweekly ERT with alglucosidase alfa (Myozyme™, 20 mg/kg KG i.v.). In two patients, stapedius reflex thresholds were also assessed before ERT-onset. Muscle tension of the stapedius and tensor tympani muscles were determined by measuring acoustic impedance at the tympanic membrane in response to single bursts of 0.5, 1, 2 and 4 kHz tones. Reflex thresholds between 70 and 90dB HL are within the normal range; higher responses indicate impaired thresholds. Patient 1 (female, 46 years) had no stapedius reflex responses before ERT-onset, reflex thresholds of 98.8/87.5dB (right/left; R/L) after one year of ERT, and reflex thresholds of 91.3/87.5dB (R/L) after two years of ERT. Patient 2 (male, 65 years) had reflex thresholds of 98.8/93.8dB (R/L) before ERT-onset, reflex thresholds of 86.3/91.3dB (R/L) after one year of ERT, and reflex thresholds of 90.0/91.3dB (R/L) after two years of ERT. Patient 3 (female, 53 years) had reflex thresholds of 93.8dB (R) and no stapedius reflex responses (L) after one year of ERT, and reflex thresholds of 96.3/98.8dB (R/L) after two years of ERT. Patient 4 (female, 69 years) had reflex thresholds of 85.0/85.0dB (R/L) after one year of ERT, and reflex thresholds of 80.0/81.3dB (R/L) after two years of ERT. Conclusion In untreated Pompe patients, stapedius reflex testing demonstrates impaired small muscle function. After one and two years of ERT, stapedius reflex thresholds improved. Consequently, stapedius reflex testing can objectively demonstrate significant improvement of muscle function with ERT