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Abstract: The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship between the quantum max cut Hamiltonian and the representation theory of the symmetric group. The first major contribution of this paper is an extension of non-commutative Sum of Squares (ncSoS) optimization techniques to give a new hierarchy of relaxations to Quantum Max Cut. The hierarchy we present is based on optimizations over polynomials in the qubit swap operators. This is in contrast to the "standard" quantum Lasserre Hierarchy, which is based on polynomials expressed in terms of the Pauli matrices. To prove correctness of this hierarchy, we exploit a finite presentation of the algebra generated by the qubit swap operators. This presentation allows for the use of computer algebraic techniques to manipulate and simplify polynomials written in terms of the swap operators, and may be of independent interest. Surprisingly, we find that level-2 of this new hierarchy is numerically exact (up to tolerance $10^{-7}$) on all QMC instances with uniform edge weights on graphs with at most 8 vertices. The second major contribution of this paper is a polynomial-time algorithm that computes (in exact arithmetic) the maximum eigenvalue of the QMC Hamiltonian for certain graphs, including graphs that can be "decomposed" as a signed combination of cliques. A special case of the latter are complete bipartite graphs with uniform edge-weights, for which exact solutions are known from the work of Lieb and Mattis. Our methods, which use representation theory of the symmetric group, can be seen as a generalization of the Lieb-Mattis result.
Keywords: Quantum Max Cut, swap operators, noncommutative polynomials, symmetric group, Gröbner bases
Published in DiRROS: 04.06.2024; Views: 335; Downloads: 165
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Abstract: Naraščajoče zbolevanje in izboljšave pri zdravljenju bolnikov z rakom dojk prispevajo tudi k naraščajočemu številu preživelih, ki pa so bolj ogroženi za razvoj drugih kroničnih bolezni, kot so srčno-žilne bolezni, bolezni dihal, povečanje telesne mase in osteoporoza. Ker se večina bolnikov zdravi tudi z radioterapijo, lahko iz slik, pridobljenih z računalniško tomografijo za namene načrtovanja obsevanja, izluščimo tudi informacije o dejavnikih tveganja za druge bolezni. Cilj projekta ARTILLERY v sklopu okvirnega programa Evropske unije Obzorje Evropa je razvoj in vrednotenje zanesljivih in zaupanja vrednih računalniško podprtih sistemov umetne inteligence, ki jih bo mogoče uporabiti na rutinsko pridobljenih računalniško tomografskih slikah za odkrivanje kroničnih bolezni ali njihovih dejavnikov tveganja za namene podaljševanja pričakovane življenjske dobe in izboljšanja kakovosti življenja v naraščajoči populaciji preživelih bolnikov z rakom dojk. V Laboratoriju za slikovne tehnologije na Fakulteti za elektrotehniko Univerze v Ljubljani imamo dolgoletne izkušnje z razvojem in vrednotenjem računalniško podprtih metod za analizo medicinskih slik hrbtenice, zato je naša vloga pri projektu povezana z določanjem tveganja osteoporoze in osteopenije ter razpoznavanjem vretenčnih zlomov. Kljub temu, da je projekt šele v začetni fazi, smo razvili računalniško podprto metodo na osnovi umetne inteligence za segmentacijo hrbtenice in določanje področij zanimanja znotraj vretenčnih teles, na podlagi katerih bomo izluščili informacije o mineralni kostni gostoti ter jo povezali z referenčnimi diagnostičnimi izvidi. Rezultati začetnih raziskav kažejo, da bo razvita metoda potencialno uporabna za zgodnje odkrivanje osteoporoze in osteopenije ter za razpoznavanje vretenčnih zlomov.
Keywords: umetna inteligenca, globoko učenje, analiza medicinskih slik, rak dojke, osteoporoza
Published in DiRROS: 04.06.2024; Views: 513; Downloads: 116
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Abstract: Well-characterized reference materials support harmonization and accuracy when conducting nucleic acid-based tests (such as qPCR); digital PCR (dPCR) can measure the absolute concentration of a specific nucleic acid sequence in a background of non-target sequences, making it ideal for the characterization of nucleic acid-based reference materials. National Metrology Institutes are increasingly using dPCR to characterize and certify their reference materials, as it offers several advantages over indirect methods, such as UV-spectroscopy. While dPCR is gaining widespread adoption, it requires optimization and has certain limitations and considerations that users should be aware of when characterizing reference materials. This review highlights the technical considerations of dPCR, as well as its role when developing and characterizing nucleic acid-based reference materials.
Keywords: digital PCR, dPCR, reference materials, UV-spectroscopy
Published in DiRROS: 03.06.2024; Views: 504; Downloads: 188
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Abstract: The increasing frequency of cyanobacteria blooms in waterbodies caused by ecosystem eutrophication could endanger human health. This risk can be mitigated by effective monitoring incorporating molecular methods. To date, most molecular studies on toxigenic cyanobacteria have been limited to microcystins (MCs), disregarding other cyanotoxins, to freshwater planktic habitats while ignoring benthic habitats, and to limited geographic areas (usually one or a few specific waterbodies). In this study, we used PCR-based methods including PCR product sequencing and chemical-analytical methods (LC-MS/MS) to screen many plankton (n = 123) and biofilm samples (n = 113) originating from 29 Alpine lakes and 18 rivers for their cyanotoxin production potential. Both mcyE (indicating MC synthesis) and anaC (indicating anatoxin (ATX) synthesis) gene fragments were able to qualitatively predict MC or ATX occurrence. The abundance of mcyE gene fragments was significantly related to MC concentrations in plankton samples (R2 = 0.61). mcyE gene fragments indicative of MC synthesis were most abundant in planktic samples (65 %) and were assigned to the genera Planktothrix and Microcystis. However, mcyE rarely occurred in biofilms of lakes and rivers, i.e., 4 % and 5 %, respectively, and were assigned to Microcystis, Planktothrix, and Nostoc. In contrast, anaC gene fragments occurred frequently in planktic samples (14 % assigned to Tychonema, Phormidium (Microcoleus), and Oscillatoria), but also in biofilms of lakes (49 %) and rivers (18 %) and were assigned to the genera Phormidium, Oscillatoria, and Nostocales. The cyrJ gene fragment indicating cylindrospermopsin synthesis occurred only once in plankton (assigned to Dolichospermum), while saxitoxin synthesis potential was not detected. For plankton samples, monomictic and less eutrophic conditions were positively related to mcyE/MC occurrence frequency, while oligomictic conditions were related to anaC/ATX frequency. The anaC/ATX frequency in biofilm was related to the lake habitats generally showing higher biodiversity as revealed from metabarcoding in a parallel study.
Keywords: cyanotoxins, planktic and benthic habitats, water quality monitoring, early warning, toxigenic cyanobacteria, European Alps
Published in DiRROS: 03.06.2024; Views: 507; Downloads: 315
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Abstract: Bisphenol A alternatives are manufactured as potentially less harmful substitutes of bisphenol A (BPA) that offer similar functionality. These alternatives are already in the market, entering the environment and thus raising ecological concerns. However, it can be expected that levels of BPA alternatives will dominate in the future, they are limited information on their environmental safety. The EU PARC project highlights BPA alternatives as priority chemicals and consolidates information on BPA alternatives, with a focus on environmental relevance and on the identification of the research gaps. The review highlighted aspects and future perspectives. In brief, an extension of environmental monitoring is crucial, extending it to cover BPA alternatives to track their levels and facilitate the timely implementation of mitigation measures. The biological activity has been studied for BPA alternatives, but in a non-systematic way and prioritized a limited number of chemicals. For several BPA alternatives, the data has already provided substantial evidence regarding their potential harm to the environment. We stress the importance of conducting more comprehensive assessments that go beyond the traditional reproductive studies and focus on overlooked relevant endpoints. Future research should also consider mixture effects, realistic environmental concentrations, and the long-term consequences on biota and ecosystems.
Keywords: BPA alternatives, biological activity, in silico, invertebrates, vertebrates, toxicity
Published in DiRROS: 03.06.2024; Views: 443; Downloads: 362
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