On the split structure of lifted groups

Let ▫$wp colon tilde{X} to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$rm{CT}_wp$▫ being abelian. Assuming that a group of automorphisms ▫$G le rm{Aut} X$▫ lifts along $wp$ to a group ▫$tilde{G} le rm{Aut} tilde{X}$▫, the problem whether the corresponding exact sequence ▫$rm{id} to rm{CT}_wp to tilde{G} to G to rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$tilde{G}$▫ nor the action ▫$Gto rm{Aut} rm{CT}_wp$▫ nor a 2-cocycle ▫$G times G to rm{CT}_wp$▫, are given. Explicitly constructing the cover ▫$tilde{X}$▫ together with ▫$rm{CT}_wp$▫ and ▫$tilde{G}$▫ as permutation groups on ▫$tilde{X}$▫ is time and space consuming whenever ▫$rm{CT}_wp$▫ is largethus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group)one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$rm{CT}_wp$▫ is elementary abelian.Naj bo ▫$wp colon tilde{X} to X$▫ regularna krovna projekcija povezanih grafov, grupa krovnih transformacij ▫$rm{CT}_wp$▫ pa naj bo abelova. Ob predpostavki, da se grupa avtomorfizmov ▫$G le rm{Aut} X$▫ dvigne vzdolž ▫$wp$▫ do grupe ▫$tilde{G} le rm{Aut} tilde{X}$▫, podrobno analiziramo problem, ali se ustrezno eksaktno zaporedje ▫$rm{id} to rm{CT}_wp to tilde{G} to G to rm{id}$▫ razcepi glede na Cayleyevo dodelitev napetosti, ki rekonstruira projekcijo do ekvivalence natančno. V gornjem kombinatoričnem sestavu je razširitev podana samo implicitno: podani niso ne ▫$tilde{G}$▫ ne delovanje ▫$Gto rm{Aut} rm{CT}_wp$▫ ne 2-kocikel ▫$G times G to rm{CT}_wp$▫. Eksplicitno konstruiranje krova ▫$tilde{X}$▫ ter ▫$rm{CT}_wp$▫ in ▫$tilde{G}$▫ kot permutacijskih grup na ▫$tilde{X}$▫ je časovno in prostorsko zahtevno vselej, kadar je ▫$rm{CT}_wp$▫ veliktako je uporaba implementiranih algoritmov (na primer, HasComplement v Magmi) vse prej kot optimalna. Namesto tega pokažemo, da lahko najnujnejšo informacijo o delovanju in 2-kociklu učinkovito izluščimo neposredno iz napetosti (ne da bi eksplicitno konstruirali krov in dvignjeno grupo)zdaj bi bilo mogoče uporabiti standardno metodo reduciranja problema na reševanje sistema linearnih enačb nad celimi števili. Vendar tukaj uberemo malce drugačen pristop, ki sploh ne zahteva nobenega poznavanja kohomologije. Časovno in prostorsko zahtevnost formalno analiziramo za vse primere, ko je ▫$rm{CT}_wp$▫ elementarna abelova

P4‐570: Repeated Baseline Eeg Measures Are Effective For Discrimination Of Amnestic From Non‐Amnestic Mci Patients

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153097/1/alzjjalz201908117.pd

P3‐455: Eeg Topology Combined With Computer Based Cognitive Assessment As Screening Tool For Cognitive Decline

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152558/1/alzjjalz2019063490.pd

Soft nanotechnology: the potential of polyelectrolyte multilayers against E. coli adhesion to surfaces

Preprečevanje adhezije bakterij na površine je najbolj učinkovit način obvladovanja rasti biofilmov. Namen te raziskave je bil analizirati anti-adhezivni potencial 5 in 50 mmol/L polielektrolitskih plasti poli(alilamin hidroklorid)/poli(natrijev 4-stirensulfonat), poli(4-vinil-N-etilpiridin bromid/ poli(natrijev 4-stirensulfonat) in poli(4-vinil-N-izobutilpiridin bromid/ poli(natrijev 4-stirensulfonat) na bakterijo E. coli. Pet zaporednih plasti polielektrolitov je bilo sestavljenih na steklenih površinah in izpostavljenih bakterijski suspenziji. Rezultati kažejo, da 50 mmol/L poli(4-vinil-N-etilpiridin bromid/ poli(natrijev 4-stirensulfonat) najbolj učinkovito prepreči adhezijo bakterij 0,4 log bakt./mm2 (60 %), sledi mu poli(4- vinil-N-izobutilpiridin bromid/ poli(natrijev 4-stirensulfonat) 0,3 log bakt. mm-2 (47 %) in poli(alilamin hidroklorid)/ poli(natrijev 4-stirensulfonat) 0,2 log bakt. mm-2 (38 %). Ta raziskava dokazuje, da polieletrolitske plasti z kvartarne amino skupinami igrajo pomembno vlogo pri preprečevanju adhezije bakterij in zato predstavljajo pomembno uporabo v živilski in farmacevtski industriji ter v medicini.Preventing bacterial attachment to surfaces is the most efficient approach to controlling biofilm proliferation. The aim of this study was to compare anti-adhesion potentials of 5 and 50 mmol/L polyelectrolyte multilayers of poly(allylamine hydrochloride)/poly(sodium 4–styrenesulfonate), poly(4-vinyl-N-ethylpyridinium bromide)/ poly(sodium 4–styrenesulfonate), and poly(4-vinyl-N-isobutylpyridinium bromide)/poly(sodium 4–styrenesulfonate) against Escherichia coli. Glass surface was covered with five polyelectrolyte layers and exposed to bacterial suspensions. Poly(4-vinyl-N-ethylpyridinium bromide)/poly(sodium 4–styrenesulfonate) was the most effective against bacterial adhesion, having reduced it by 60 %, followed by poly(4-vinyl-N-isobutylpyridinium bromide)/poly(sodium 4– styrenesulfonate) (47 %), and poly(allylamine hydrochloride)/poly(sodium 4–styrenesulfonate) (38 %). Polyelectrolyte multilayers with quaternary amine groups have a significant anti-adhesion potential and could find their place in coatings for food, pharmaceutical, and medical industry

Sectional split extensions arising from lifts of groups

Covering techniques have recently emerged as an effective tool used for classification of several infinite families of connected symmetric graphs. One commonly encountered technique is based on the concept of lifting groups of automorphisms along regular covering projections ▫$wp colon tilde{X} to X$▫. Efficient computational methods are known for regular covers with cyclic or elementary abelian group of covering transformations CT▫$(wp)$▫. In this paper we consider the lifting problem with an additional condition on how a group should lift: given a connected graph ▫$X$▫ and a group ▫$G$▫ of its automorphisms, find all connected regular covering projections ▫$wp colon tilde{X} to X$▫ along which ▫$G$▫ lifts as a sectional split extension. By this we mean that there exists a complement ▫$overline{G}$▫ of CT▫$(wp)$▫ within the lifted group ▫$tilde{G}$▫ such that ▫$overline{G}$▫ has an orbit intersecting each fibre in at most one vertex. As an application, all connected elementary abelian regular coverings of the complete graph ▫$K_4$▫ along which a cyclic group of order 4 lifts as a sectional split extension are constructed.Krovne tehnike so se izkazale kot učinkovito orodje pri klasifikaciji več neskončnih družin povezanih simetričnih grafov. Ena izmed pogostih tehnik, s katerimi se srečamo, temelji na konceptu dviga avtomorfizmov grup vzdolž regularnih krovnih projekcij ▫$wp colon tilde{X} to X$▫. Učinkovite računske metode so znane v primeru regulanih krovov s ciklično ali elementarno abelsko grupo krovnih transformacij CT▫$(wp)$▫. V članku študiramo problem dviga pri dodatnem pogoju, kako naj se grupa dvigne: za dani povezan graf▫ $X$▫ in podgrupo ▫$G$▫ njegovih avtomorfizmov poišči vse povezane regularne krovne projekcije ▫$wp colon tilde{X} to X$▫, vzdolž katerih se ▫$G$▫ dvigne kot sekcijska razcepna razširitev. To pomeni, da obstajakomplement ▫$overline{G}$▫ k CT▫$(wp)$▫ znotraj dvignjene grupe ▫$tilde{G}$▫, tako da ima ▫$overline{G}$▫ orbito, ki seka vsako vlakno v največ enem vozlišču. Za ilustracijo konstruiramo vse povezane elementarno ableske regularne krove polnega grafa ▫$K_4$▫, vzdolž katerih se ciklična grupa reda 4 dvigne kot sekcijska razcepna razširitev

Testiranje razcepnosti dvignjene grupe

Let a group of automorphisms lift along a regular covering projection of connected graphs given combinatorially by means of voltages. The data that determine the lifted group and its action are then conveniently encoded in terms of voltages as well. Along these lines, an algorithm for testing whether the lifted group is a split extension of the group of covering transformations has recently been proposed in the case when the group of covering transformations is solvable. It consists of decomposing the covering into a series of coverings with elementary abelian groups of covering transformations, and inductively solving the problem at every elementary abelian step. Although the explicit construction of the lifted group is not needed, it still involves time and space consuming constructions of certain subgroups in the lifted group at every step except at the final one. In this paper, an improved version that completely avoids such constructions is presented. From voltage distribution we first compute the weak action and the factor set that determine the lifted group, and we then carry out the test by extracting the necessary information only from the corresponding weak actions and factor sets at every step. An experimental comparison is made against the previous version.Naj se grupa avtomorfizmov dvigne vzdolž regularne krovne projekcije povezanih grafov, podane kombinatorično z napetostmi. Tedaj so podatki, ki določajo dvignjeno grupo in njeno delovanje, prav tako zakodirani s pomočjo napetosti. Ustrezni algoritem za testiranje, ali je dvignjena grupa razcepna razširitev grupe krovnih transformacij, je bil nedavno predstavljen v primeru, ko je grupa krovnih transformacij rešljiva. Sestoji iz dekomponiranja krova v zaporedje krovov z elementarnimi abelovimi grupami krovnih transformacij, in induktivnega reševanja problema na vsakem elementarno abelovem koraku. Čeprav eksplicitna konstrukcija dvignjene grupe ni potrebna, algoritem vseeno vključuje časovno in prostorsko zahtevne konstrukcije določenih podgrup v dvignjeni grupi na vsakem koraku z izjemo zadnjega. V tem članku predstavimo izboljšano verzijo algoritma, ki se povsem izogne takšnim konstrukcijam. Iz porazdelitve napetosti najprej izračunamo šibko delovanje in faktorsko množico, ki določata dvignjeno grupo, nato pa izpeljemo test tako, da izluščimo potrebno informacijo samo iz ustreznih šibkih delovanj in faktorskih množic na vsakem koraku. Eksperimentalno primerjamo to in prejšnjo verzijo algoritma