1. |
- Caselli, Lucrezia, et al.
(författare)
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Conformational control of antimicrobial peptide amphiphilicity : consequences for boosting membrane interactions and antimicrobial effects of photocatalytic TiO2 nanoparticles
- 2024
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Ingår i: Physical Chemistry, Chemical Physics - PCCP. - : Royal Society of Chemistry. - 1463-9076 .- 1463-9084. ; 26:23, s. 16529-16539
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Tidskriftsartikel (refereegranskat)abstract
- This study reports on the effects of conformationally controlled amphiphilicity of antimicrobial peptides (AMPs) on their ability to coat TiO2 nanoparticles (NPs) and boost the photocatalytic antimicrobial effects of such NPs. For this, TiO2 NPs were combined with AMP EFK17 (EFKRIVQRIKDFLRNLV), displaying a disordered conformation in aqueous solution but helix formation on interaction with bacterial membranes. The membrane-bound helix is amphiphilic, with all polar and charged amino acid residues located at one side and all non-polar and hydrophobic residues on the other. In contrast, the d-enantiomer variant EFK17-d (E(dF)KR(dI)VQR(dI)KD(dF)LRNLV) is unable to form the amphiphilic helix on bacterial membrane interaction, whereas the W-residues in EFK17-W (EWKRWVQRWKDFLRNLV) boost hydrophobic interactions of the amphiphilic helix. Circular dichroism results showed the effects displayed for the free peptide, to also be present for peptide-coated TiO2 NPs, causing peptide binding to decrease in the order EFK17-W > EFK17 > EFK17-d. Notably, the formation of reactive oxygen species (ROS) by the TiO2 NPs was essentially unaffected by the presence of peptide coating, for all the peptides investigated, and the coatings stabilized over hours of UV exposure. Photocatalytic membrane degradation from TiO2 NPs coated with EFK17-W and EFK17 was promoted for bacteria-like model bilayers containing anionic phosphatidylglycerol but suppressed in mammalian-like bilayers formed by zwitterionic phosphatidylcholine and cholesterol. Structural aspects of these effects were further investigated by neutron reflectometry with clear variations observed between the bacteria- and mammalian-like model bilayers for the three peptides. Mirroring these results in bacteria-like model membranes, combining TiO2 NPs with EFK17-W and EFK17, but not with non-adsorbing EFK17-d, resulted in boosted antimicrobial effects of the resulting cationic composite NPs already in darkness, effects enhanced further on UV illumination.
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2. |
- Caselli, Lucrezia, et al.
(författare)
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Conformational control of antimicrobial peptide amphiphilicity : consequences for boosting membrane interactions and antimicrobial effects of photocatalytic TiO2 nanoparticles
- 2024
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Ingår i: Physical Chemistry Chemical Physics. - : Royal Society of Chemistry. - 1463-9076 .- 1463-9084. ; 26:23, s. 16529-16539
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Tidskriftsartikel (refereegranskat)abstract
- This study reports on the effects of conformationally controlled amphiphilicity of antimicrobial peptides (AMPs) on their ability to coat TiO2 nanoparticles (NPs) and boost the photocatalytic antimicrobial effects of such NPs. For this, TiO2 NPs were combined with AMP EFK17 (EFKRIVQRIKDFLRNLV), displaying a disordered conformation in aqueous solution but helix formation on interaction with bacterial membranes. The membrane-bound helix is amphiphilic, with all polar and charged amino acid residues located at one side and all non-polar and hydrophobic residues on the other. In contrast, the d-enantiomer variant EFK17-d (E(dF)KR(dI)VQR(dI)KD(dF)LRNLV) is unable to form the amphiphilic helix on bacterial membrane interaction, whereas the W-residues in EFK17-W (EWKRWVQRWKDFLRNLV) boost hydrophobic interactions of the amphiphilic helix. Circular dichroism results showed the effects displayed for the free peptide, to also be present for peptide-coated TiO2 NPs, causing peptide binding to decrease in the order EFK17-W > EFK17 > EFK17-d. Notably, the formation of reactive oxygen species (ROS) by the TiO2 NPs was essentially unaffected by the presence of peptide coating, for all the peptides investigated, and the coatings stabilized over hours of UV exposure. Photocatalytic membrane degradation from TiO2 NPs coated with EFK17-W and EFK17 was promoted for bacteria-like model bilayers containing anionic phosphatidylglycerol but suppressed in mammalian-like bilayers formed by zwitterionic phosphatidylcholine and cholesterol. Structural aspects of these effects were further investigated by neutron reflectometry with clear variations observed between the bacteria- and mammalian-like model bilayers for the three peptides. Mirroring these results in bacteria-like model membranes, combining TiO2 NPs with EFK17-W and EFK17, but not with non-adsorbing EFK17-d, resulted in boosted antimicrobial effects of the resulting cationic composite NPs already in darkness, effects enhanced further on UV illumination.
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3. |
- Chmiel, Hannah Elisa, 1983-, et al.
(författare)
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The role of sediments in the carbon budget of a small boreal lake
- 2016
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Ingår i: Limnology and Oceanography. - : Wiley. - 0024-3590 .- 1939-5590. ; 61:5, s. 1814-1825
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Tidskriftsartikel (refereegranskat)abstract
- We investigated the role of lake sediments as carbon (C) source and sink in the annual C budget of a small (0.07 km2), shallow (mean depth 3.4 m), and humic lake (mean DOC concentration 17 mg L-1) in boreal Sweden. Organic carbon (OC) burial and mineralization in sediments were quantified from 210Pb-dated sediment and laboratory sediment incubation experiments, respectively, and upscaled to the entire basin and to one whole year, by using sediment thickness derived sub-bottom profiling, basin morphometry, and water column monitoring data of temperature and oxygen concentration. Furthermore, catchment C import, open water metabolism, photochemical mineralization as well as carbon dioxide (CO2) and methane (CH4) emissions to the atmosphere, were quantified to relate sediment processes to other lake C fluxes. We found that on a whole-basin and annual scale, sediment OC mineralization was three times larger than OC burial, and contributed about 16% to the annual CO2 emission from the lake to the atmosphere. Remaining contributions to the CO2 emission were attributed to water column metabolism (31%), photochemical mineralization (6%), and catchment imports via inlet streams and inflow of shallow groundwater (47%). We conclude that on an annual and whole-basin scale 1) sediment OC mineralization dominated over OC burial, 2) water column OC mineralization contributed more than sediments to lake CO2 emission, and 3) catchment import of C to the lake was greater than lake-internal C cycling.
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4. |
- Deans, Andrew R, et al.
(författare)
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Finding Our Way through Phenotypes.
- 2015
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Ingår i: PLoS Biology. - : Public Library of Science (PLoS). - 1545-7885. ; 13:1
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Tidskriftsartikel (refereegranskat)abstract
- Despite a large and multifaceted effort to understand the vast landscape of phenotypic data, their current form inhibits productive data analysis. The lack of a community-wide, consensus-based, human- and machine-interpretable language for describing phenotypes and their genomic and environmental contexts is perhaps the most pressing scientific bottleneck to integration across many key fields in biology, including genomics, systems biology, development, medicine, evolution, ecology, and systematics. Here we survey the current phenomics landscape, including data resources and handling, and the progress that has been made to accurately capture relevant data descriptions for phenotypes. We present an example of the kind of integration across domains that computable phenotypes would enable, and we call upon the broader biology community, publishers, and relevant funding agencies to support efforts to surmount today's data barriers and facilitate analytical reproducibility.
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5. |
- Del Giudice, Alessandra, et al.
(författare)
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Towards natural care products : Structural and deposition studies of bio-based polymer and surfactant mixtures
- 2024
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Ingår i: Colloids and Surfaces A: Physicochemical and Engineering Aspects. - : Elsevier. - 0927-7757 .- 1873-4359. ; 698
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Tidskriftsartikel (refereegranskat)abstract
- Oppositely charged polymer-surfactant systems are expected to interact with formation of coacervate complexes near composition of charge-neutrality. Such behaviour is widely used in formulated products (e.g. household and personal care), where the co-deposition of coacervates and active ingredients on various surfaces is triggered by dilution. A transition towards the use of more sustainable ingredients is currently ongoing as a response to the need of more environmentally conscious choices in production, albeit slowed down by the often more complex and not fully understood bulk and interfacial behaviour of new ingredients. In this work, mixtures of a medium-chain fatty acid (sodium decanoate) and two grades of bio-based cationic modified inulin were studied. The phase behaviour was determined in a wide composition matrix. The formation of coacervate complexes was observed for the mixture with the higher charge density polymer at a surfactant concentration of 1–3 wt%, close to the surfactant critical micellar concentration in pure water. Such behaviour was confirmed by DLS and SAXS data, suggesting surfactant-polymer complexation in a concentrated phase of packed micelles with a micelle-to-micelle distance of ∼4.5 nm. In situ ellipsometry and neutron reflectometry experiments were conducted to study the effect on surface deposition when diluting. The ellipsometry showed an adsorbed mass of ∼1.3–1.9 mg/m2, consistent with the deposition of a coacervate layer, and considerably higher than the neat, adsorbed polymer layer of ∼0.3 mg/m2. In the case of the neutron reflectometry experiments, dilution was performed before contact with the surface (pre-mixing), and no adsorption of coacervates was observed, but rather the adsorption of a polymer layer (0.49–0.85 mg/m2). The different results obtained with the different techniques highlight the kinetic nature of bulk coacervate formation and deposition, and the competition between these two phenomena. Maximal deposition can be achieved if one can control this time window either by tuning the composition of the system or the experimental set-up, to mimic the conditions of a specific application.
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6. |
- Gudasz, Cristian, et al.
(författare)
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Temperature sensitivity of organic carbon mineralization in contrasting lake sediments
- 2015
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Ingår i: Journal of Geophysical Research - Biogeosciences. - : American Geophysical Union (AGU). - 2169-8953 .- 2169-8961. ; 120:7, s. 1215-1225
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Tidskriftsartikel (refereegranskat)abstract
- Temperature alone explains a great amount of variation in sediment organic carbon (OC) mineralization. Studies on decomposition of soil OC suggest that (1) temperature sensitivity differs between the fast and slowly decomposition OC and (2) over time, decreasing soil respiration is coupled with increase in temperature sensitivity. In lakes, autochthonous and allochthonous OC sources are generally regarded as fast and slowly decomposing OC, respectively. Lake sediments with different contributions of allochthonous and autochthonous components, however, showed similar temperature sensitivity in short-term incubation experiments. Whether the mineralization of OC in lake sediments dominated by allochthonous or autochthonous OC has different temperature sensitivity in the longer term has not been addressed. We incubated sediments from two boreal lakes that had contrasting OC origin (allochthonous versus autochthonous), and OC characteristics (C/N ratios of 21 and 10) at 1, 3, 5, 8, 13, and 21 degrees C for five months. Compared to soil and litter mineralization, sediment OC mineralization rates were low in spite of low apparent activation energy (E-a). The fraction of the total OC pool that was lost during five months varied between 0.4 and 14.8%. We estimate that the sediment OC pool not becoming long-term preserved was degraded with average apparent turnover times between 3 and 32years. While OC mineralization was strongly dependent on temperature as well as on OC composition and origin, temperature sensitivity was similar across lakes and over time. We suggest that the temperature sensitivity of OC mineralization in lake sediments is similar across systems within the relevant seasonal scales of OC supply and degradation.
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7. |
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8. |
- Jansen, Willemijn J, et al.
(författare)
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Association of Cerebral Amyloid-β Aggregation With Cognitive Functioning in Persons Without Dementia.
- 2018
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Ingår i: JAMA psychiatry. - : American Medical Association (AMA). - 2168-6238 .- 2168-622X. ; 75:1, s. 84-95
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Tidskriftsartikel (refereegranskat)abstract
- Cerebral amyloid-β aggregation is an early event in Alzheimer disease (AD). Understanding the association between amyloid aggregation and cognitive manifestation in persons without dementia is important for a better understanding of the course of AD and for the design of prevention trials.To investigate whether amyloid-β aggregation is associated with cognitive functioning in persons without dementia.This cross-sectional study included 2908 participants with normal cognition and 4133 with mild cognitive impairment (MCI) from 53 studies in the multicenter Amyloid Biomarker Study. Normal cognition was defined as having no cognitive concerns for which medical help was sought and scores within the normal range on cognitive tests. Mild cognitive impairment was diagnosed according to published criteria. Study inclusion began in 2013 and is ongoing. Data analysis was performed in January 2017.Global cognitive performance as assessed by the Mini-Mental State Examination (MMSE) and episodic memory performance as assessed by a verbal word learning test. Amyloid aggregation was measured with positron emission tomography or cerebrospinal fluid biomarkers and dichotomized as negative (normal) or positive (abnormal) according to study-specific cutoffs. Generalized estimating equations were used to examine the association between amyloid aggregation and low cognitive scores (MMSE score ≤27 or memory z score≤-1.28) and to assess whether this association was moderated by age, sex, educational level, or apolipoprotein E genotype.Among 2908 persons with normal cognition (mean [SD] age, 67.4 [12.8] years), amyloid positivity was associated with low memory scores after age 70 years (mean difference in amyloid positive vs negative, 4% [95% CI, 0%-7%] at 72 years and 21% [95% CI, 10%-33%] at 90 years) but was not associated with low MMSE scores (mean difference, 3% [95% CI, -1% to 6%], P=.16). Among 4133 patients with MCI (mean [SD] age, 70.2 [8.5] years), amyloid positivity was associated with low memory (mean difference, 16% [95% CI, 12%-20%], P<.001) and low MMSE (mean difference, 14% [95% CI, 12%-17%], P<.001) scores, and this association decreased with age. Low cognitive scores had limited utility for screening of amyloid positivity in persons with normal cognition and those with MCI. In persons with normal cognition, the age-related increase in low memory score paralleled the age-related increase in amyloid positivity with an intervening period of 10 to 15 years.Although low memory scores are an early marker of amyloid positivity, their value as a screening measure for early AD among persons without dementia is limited.
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9. |
- Jansen, Willemijn J, et al.
(författare)
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Prevalence of cerebral amyloid pathology in persons without dementia: a meta-analysis.
- 2015
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Ingår i: JAMA. - : American Medical Association (AMA). - 1538-3598 .- 0098-7484. ; 313:19, s. 1924-38
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Tidskriftsartikel (refereegranskat)abstract
- Cerebral amyloid-β aggregation is an early pathological event in Alzheimer disease (AD), starting decades before dementia onset. Estimates of the prevalence of amyloid pathology in persons without dementia are needed to understand the development of AD and to design prevention studies.
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10. |
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11. |
- Köhler, Thomas, et al.
(författare)
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Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces
- 2021
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Ingår i: SciPost Physics. - : SCIPOST FOUNDATION. - 2542-4653. ; 10:3
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Tidskriftsartikel (refereegranskat)abstract
- Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L = 501 while accounting for N-ph = 63 phonons per site with high precision in the CDW phase.
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12. |
- Paeckel, Sebastian, et al.
(författare)
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Detecting superconductivity out of equilibrium
- 2020
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 101:18
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Tidskriftsartikel (refereegranskat)abstract
- Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above T-c. This poses the question of how to reliably identify the emergence of long-range order, in particular superconductivity, out of equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved angle-resolved photoemission spectroscopy experiments to probe for the formation of a condensate in the two-particle channel.
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13. |
- Paeckel, Sebastian, et al.
(författare)
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Time-evolution methods for matrix-product states
- 2019
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Ingår i: Annals of Physics. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0003-4916 .- 1096-035X. ; 411
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Tidskriftsartikel (refereegranskat)abstract
- Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W-I,W-II method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics. (C) 2019 The Author(s). Published by Elsevier Inc.
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14. |
- Peters, Ruth, et al.
(författare)
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An investigation of antihypertensive class, dementia, and cognitive decline: A meta-analysis.
- 2020
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Ingår i: Neurology. - 1526-632X. ; 94:3
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Tidskriftsartikel (refereegranskat)abstract
- High blood pressure is one of the main modifiable risk factors for dementia. However, there is conflicting evidence regarding the best antihypertensive class for optimizing cognition. Our objective was to determine whether any particular antihypertensive class was associated with a reduced risk of cognitive decline or dementia using comprehensive meta-analysis including reanalysis of original participant data.To identify suitable studies, MEDLINE, Embase, and PsycINFO and preexisting study consortia were searched from inception to December 2017. Authors of prospective longitudinal human studies or trials of antihypertensives were contacted for data sharing and collaboration. Outcome measures were incident dementia or incident cognitive decline (classified using the reliable change index method). Data were separated into mid and late-life (>65 years) and each antihypertensive class was compared to no treatment and to treatment with other antihypertensives. Meta-analysis was used to synthesize data.Over 50,000 participants from 27 studies were included. Among those aged >65 years, with the exception of diuretics, we found no relationship by class with incident cognitive decline or dementia. Diuretic use was suggestive of benefit in some analyses but results were not consistent across follow-up time, comparator group, and outcome. Limited data precluded meaningful analyses in those ≤65 years of age.Our findings, drawn from the current evidence base, support clinical freedom in the selection of antihypertensive regimens to achieve blood pressure goals.The review was registered with the international prospective register of systematic reviews (PROSPERO), registration number CRD42016045454.
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15. |
- Salvaneschi, Guido, et al.
(författare)
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Language-integrated privacy-aware distributed queries
- 2019
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Ingår i: Proceedings of the ACM on Programming Languages. - : Association for Computing Machinery (ACM). - 2475-1421. ; 3:OOPSLA, s. 167:1-167:30
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Tidskriftsartikel (refereegranskat)abstract
- Distributed query processing is an effective means for processing large amounts of data. To abstract from the technicalities of distributed systems, algorithms for operator placement automatically distribute sequential data queries over the available processing units. However, current algorithms for operator placement focus on performance and ignore privacy concerns that arise when handling sensitive data.We present a new methodology for privacy-aware operator placement that both prevents leakage of sensitive information and improves performance. Crucially, our approach is based on an information-flow type system for data queries to reason about the sensitivity of query subcomputations. Our solution unfolds in two phases. First, placement space reduction generates deployment candidates based on privacy constraints using a syntax-directed transformation driven by the information-flow type system. Second, constraint solving selects the best placement among the candidates based on a cost model that maximizes performance. We verify that our algorithm preserves the sequential behavior of queries and prevents leakage of sensitive data. We implemented the type system and placement algorithm for a new query language SecQL and demonstrate significant performance improvements in benchmarks.
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16. |
- Stolpp, Jan, et al.
(författare)
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Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert spaces without U(1) symmetry
- 2021
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Ingår i: Computer Physics Communications. - : Elsevier. - 0010-4655 .- 1879-2944. ; 269
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Tidskriftsartikel (refereegranskat)abstract
- Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches.
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17. |
- Thöns, Sebastian, et al.
(författare)
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On information value and decision analyses
- 2024
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Ingår i: Structural Safety. - 0167-4730.
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses value of information, structural health information, and decision analyses in built environment engineering. Decision analyses are used for the joint optimization of information collection and the identification of physical measures for the management and enhancement of the expected utility of built environment systems. To these ends, this paper contains (1) principal descriptions of decision scenarios and the model basis in conjunction with the objective functions, embedded in (a) a summary of the historical background and (b) the origins of the methods of decision and value of information analyses, (2) an overview of methods for decision analyses highlighting solution strategies to handle comprehensiveness and computational challenges, (3) principal application areas and case studies, and (4) insights into recent advances. The main insights and an outreach to potential future research perspectives are summarised at the end of this paper.
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18. |
- Vos, Stephanie J B, et al.
(författare)
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Modifiable Risk Factors for Prevention ofDementia in Midlife, Late Life and the Oldest-Old: Validation of the LIBRA Index.
- 2017
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Ingår i: Journal of Alzheimer's disease : JAD. - 1875-8908. ; 58:2, s. 537-547
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Tidskriftsartikel (refereegranskat)abstract
- Recently, the LIfestyle for BRAin health (LIBRA) index was developed to assess an individual's prevention potential for dementia.We investigated the predictive validity of the LIBRA index for incident dementia in midlife, late life, and the oldest-old.9,387 non-demented individuals were recruited from the European population-based DESCRIPA study. An individual's LIBRA index was calculated solely based on modifiable risk factors: depression, diabetes, physical activity, hypertension, obesity, smoking, hypercholesterolemia, coronary heart disease, and mild/moderate alcohol use. Cox regression was used to test the predictive validity of LIBRA for dementia at follow-up (mean 7.2y, range 1-16).In midlife (55-69y, n=3,256) and late life (70-79y, n=4,320), the risk for dementia increased with higher LIBRA scores. Individuals in the intermediate- and high-risk groups had a higher risk of dementia than those in the low-risk group. In the oldest-old (80-97y, n=1,811), higher LIBRA scores did not increase the risk for dementia.LIBRA might be a useful tool to identify individuals for primary prevention interventions of dementia in midlife, and maybe in late life, but not in the oldest-old.
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19. |
- Wilke, Reja H., et al.
(författare)
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Symmetry-protected Bose-Einstein condensation of interacting hardcore bosons
- 2023
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Ingår i: Communications Physics. - : Springer Nature. - 2399-3650. ; 6:1
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Tidskriftsartikel (refereegranskat)abstract
- The large practical potential of exotic quantum states is often precluded by their notorious fragility against external perturbations or temperature. Here, we introduce a mechanism stabilizing a one-dimensional quantum many-body phase exploiting an emergent Z(2) -symmetry based on a simple geometrical modification, i.e. a site that couples to all lattice sites. We illustrate this mechanism by constructing the solution of the full quantum many-body problem of hardcore bosons on a wheel geometry, which are known to form Bose-Einstein condensates. The robustness of the condensate against interactions is shown numerically by adding nearest-neighbor interactions, which typically destroy Bose-Einstein condensates. We discuss further applications such as geometrically inducing finite-momentum condensates. Since our solution strategy is based on a generic mapping, our findings are applicable in a broader context, in which a particular state should be protected, by introducing an additional center site.
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