On Polygons Excluding Point Sets

By a polygonization of a finite point set $S$ in the plane we understand a simple polygon having $S$ as the set of its vertices. Let $B$ and $R$ be sets of blue and red points, respectively, in the plane such that $B\cup R$ is in general position, and the convex hull of $B$ contains $k$ interior blue points and $l$ interior red points. Hurtado et al. found sufficient conditions for the existence of a blue polygonization that encloses all red points. We consider the dual question of the existence of a blue polygonization that excludes all red points $R$. We show that there is a minimal number $K=K(l)$, which is polynomial in $l$, such that one can always find a blue polygonization excluding all red points, whenever $k\geq K$. Some other related problems are also considered.Comment: 14 pages, 15 figure

Semidistributivity, Constraint Satisfaction Problem and strong Mal’cev conditions

U ovoj tezi opisujemo linearne, idempotentne, jake Maljcevljeve uslove za kongruencijsku ^-poludistributivnost u lokalno konačnim varijetetima. U [40] je predstavljen jedan takav jak Maljcevljev uslov i tehnika koju su autori koristili je uopštenje jednog od glavnih rezultata iz [46]. Glavna razlika je u tome što jednostavna primjena Dirihleovog principa u [46] postaje dosta komplikovaniji argument Remzijevskog tipa u [40]. Mi ovdje dodatno uopštavamo taj argument i prezentujemo dokaz pomenute karakterizacije. Svi ovi radovi koriste snažan rezultat [4] L. Barta o rješivosti Problema zadovoljenja uslova metodama provjere lokalne konzistencije uslova, pa je treća glava teze posvećena detaljnoj prezentaciji tog rada. Takođe, dokazujemo da neki jak Maljcevljev uslov karakteriše kongruencijsku ^-poludistributivnost u lokalno konačnim varijetetima ako i samo ako je realizovan u određenoj četvoroelementnoj algebri. Na kraju, bavimo se i problemom pronalaženja optimalnog jakog Maljcevljevog uslova koji karakteriše egzistenciju Tejlorovog terma u opštem slučaju. U [53] M. Olšak predstavio je iznenađujući rezultat da je egzistencija Tejlorovog terma jako Maljcevljevo svojstvo. Term iz prvobitne verzije [53] ima arnost 12, dok mi ovdje prezentujemo dokaz da se arnost može redukovati na 9.  In this thesis we describe linear, idempotent, strong Mal’cev conditions for congruence ^-semidistributivity in locally finite varieties. In [40] authors presented one such Mal’cev  condition and technique they used is generalization of one result from [46]. Main difference is that simple application of Pigeonhole prinicple from [46] becomes much more complicated Ramsey style argument in [40]. Here we dditionaly generalize that argument and we present the proof of above mentioned characterization. All these papers use deep result [4] by L. Barto on solvability of Constraint Satisfaction Problem by local consistency checking methods, so third chapter of this thesis is dedicated to detailed presentation of [4]. Also, we prove that some strong Mal’cev condition characterizes congruence ^-semidistributivity in locally finite varieties if and only if it is realized in certain four element algebra. Finally, we work on the problem of finding optimal strong Mal’cev condition for existence of Taylor term in general case. In [53] M.  Olsak presented suprising result that exisstence of Taylor term is strong Malcev property. The term from first version of [53] has arity 12, but here we prove that arity can  be reduced to 9

Quantitative characterization in contact Hamiltonian dynamics -- I

Based on the contact Hamiltonian Floer theory established by Will J. Merry and the second author that applies to any admissible contact Hamiltonian system $(M, \xi = \ker \alpha, h)$, where $h$ is a contact Hamiltonian function on a Liouville fillable contact manifold $(M, \xi = \ker \alpha)$, we associate a persistence module to $(M, \xi, h)$, called a gapped module, that is parametrized only by a partially ordered set. It enables us to define various numerical Floer-theoretic invariants. In this paper, we focus on the contact spectral invariants and their applications. Several key properties are proved, which include stability with respect to the Shelukhin-Hofer norm in contact geometry and a triangle inequality of contact spectral invariants. In particular, our stability property does not involve any conformal factors; our triangle inequality is derived from a novel analysis on pair-of-pants in the contact Hamiltonian Floer homology. While this paper was nearing completion, the authors were made aware of upcoming work by Dylan Cant, where a similar persistence module for contact Hamiltonian dynamics was constructed.Comment: 47 pages, 1 figur

Research summary: Anxiety and Depression from Adolescence to Old Age in Autism Spectrum Disorder

[Excerpt] Our team recently published a journal article reporting on a study that looked at the relationship between anxiety and depression, age, sex (male, female), and autism symptoms in autistic adults. So far there has been little research into mental health challenges such as anxiety and depression across the lifespan of autistic individuals. To inform and provide appropriate supports we need to better understand the challenges experienced by autistic individuals and looking at mental health across the lifespan can help us do that. It is also important to understand what factors can be related to good and poor mental health, so we can investigate that relationship and understand it

The systematization of analytical and numerical methods of landslide stability calculation

Na osnovu analize mnogih naučnih radova, autori su dali prikaz sopstvene originalne sistematizacije analitičkih i numeričkih metoda proračuna stabilnosti klizišta, pri čemu mnoge od njih tek treba dodatno da se unaprede, implementiraju i testiraju na kompleksnim 3D modelima klizišta. Metode proračuna stabilnosti klizišta klasifikovane su u pet grupa: analitičke jednokoračne, analitičke višekoračne (iteracije kliznih površi), numeričke višekoračne (iteracije kliznih površi), numeričke inkrementalno-iterativne (nelinearne) analize i numeričke inkrementalno-iterativne (nelinearne) analize, uz primenu numeričke integracije u vremenskom domenu. Primenom sprovedene sistematizacije metoda proračuna stabilnosti klizišta, može se vrlo efikasno razmotriti koji je tip metode optimalan za analizu klizišta i koji tip metode je potrebno koristiti u fazi preliminarnih i finalnih analiza za naučna istraživanja i stručne projekte.According to the analysis of a large number of scientific papers, the authors of the paper presented their own original systematization of the analytical and numerical methods of landslide stability calculation, with a large part of them still to be further improved, implemented and tested on complex 3D landslide models. Methods for calculating the stability of the landslide are classified into five groups: analytical single-step, analytical multi-step (iterations of sliding surfaces), numerical multi-step (iterations of sliding surfaces), numerical incremental-iterative (nonlinear) analysis and numerical incremental-iterative (nonlinear) analysis, applying numerical integration in the time domain. By using the systematization method of calculating the stability of the landslide it can be very effective to consider which type of method is optimal for landslide analysis and which type of method should be considered in the phase of preliminary and final analysis for scientific research and expert projects

Semidistributivity, Constraint Satisfaction Problem and strong Mal’cev conditions

U ovoj tezi opisujemo linearne, idempotentne, jake Maljcevljeve uslove za kongruencijsku ^-poludistributivnost u lokalno konačnim varijetetima. U [40] je predstavljen jedan takav jak Maljcevljev uslov i tehnika koju su autori koristili je uopštenje jednog od glavnih rezultata iz [46]. Glavna razlika je u tome što jednostavna primjena Dirihleovog principa u [46] postaje dosta komplikovaniji argument Remzijevskog tipa u [40]. Mi ovdje dodatno uopštavamo taj argument i prezentujemo dokaz pomenute karakterizacije. Svi ovi radovi koriste snažan rezultat [4] L. Barta o rješivosti Problema zadovoljenja uslova metodama provjere lokalne konzistencije uslova, pa je treća glava teze posvećena detaljnoj prezentaciji tog rada. Takođe, dokazujemo da neki jak Maljcevljev uslov karakteriše kongruencijsku ^-poludistributivnost u lokalno konačnim varijetetima ako i samo ako je realizovan u određenoj četvoroelementnoj algebri. Na kraju, bavimo se i problemom pronalaženja optimalnog jakog Maljcevljevog uslova koji karakteriše egzistenciju Tejlorovog terma u opštem slučaju. U [53] M. Olšak predstavio je iznenađujući rezultat da je egzistencija Tejlorovog terma jako Maljcevljevo svojstvo. Term iz prvobitne verzije [53] ima arnost 12, dok mi ovdje prezentujemo dokaz da se arnost može redukovati na 9.  In this thesis we describe linear, idempotent, strong Mal’cev conditions for congruence ^-semidistributivity in locally finite varieties. In [40] authors presented one such Mal’cev  condition and technique they used is generalization of one result from [46]. Main difference is that simple application of Pigeonhole prinicple from [46] becomes much more complicated Ramsey style argument in [40]. Here we dditionaly generalize that argument and we present the proof of above mentioned characterization. All these papers use deep result [4] by L. Barto on solvability of Constraint Satisfaction Problem by local consistency checking methods, so third chapter of this thesis is dedicated to detailed presentation of [4]. Also, we prove that some strong Mal’cev condition characterizes congruence ^-semidistributivity in locally finite varieties if and only if it is realized in certain four element algebra. Finally, we work on the problem of finding optimal strong Mal’cev condition for existence of Taylor term in general case. In [53] M.  Olsak presented suprising result that exisstence of Taylor term is strong Malcev property. The term from first version of [53] has arity 12, but here we prove that arity can  be reduced to 9

FIBER REINFORCED SHOTCRETE - THE BENEFITS OF THE APPLICATION IN TUNNEL BUILDING

Poboljšavanjem fizičko-mehaničkih svojstava betona, dodatkom vlakana, osigurava se sve šira primjena takvog kompozita, u realnim projektima. Tehnološki razvoj opreme za ugradnju betona prskanjem, omogućio je upotrebu mikroarmiranog betona, u prvom redu u konstruktivnim sistemima osiguranja iskopa podzemnih konstrukcija. U radu će se prikazati rezultati ispitivanja fizičko-mehaničkih svojstava betonskih mješavina s čeličnim vlaknima. Specificirati će se prednosti primjene ovakvog kompozita u izradi obloga podzemnih konstrukcija. Prikazati će se preporuke za spravljanje i ugrađivanje mikroarmiranog betona tehnologijom prskanja, kao i pristup u dimenzioniranju tunelske obloge od mikroarmiranog betona.Fibers enhance the psysical and mechanical properties of concrete and bring wider application of such composite in real projects. The technological development of equipment for the installation of concrete by spraying enabled the use of micro-reinforced concrete, primarily in constructive systems for ensuring the excavation of underground structures. The paper will present the results of testing physical and mechanical properties of concrete mixtures with steel fibers. Тhe adventages of using such a composite on lining of underground structures will be specified. Recommendations for making and installation of micro-reinforced concrete with spraying technology, as well as the approach to dimensioning the tunnel lining made of micro-reinforced concrete will be presented

Profiles of circumscribed interests in autistic youth

Circumscribed interests (CI) encompass a range of different interests and related behaviors that can be characterized by either a high intensity but otherwise usual topic [referred to as restricted interests (RI)] or by a focus on topics that are not salient outside of autism [referred to as unusual interests (UI)]. Previous research has suggested that there is pronounced variability across individuals in terms of the endorsement of different interests, however, this variability has not been quantified using formal subtyping approaches. Therefore, using Latent Profile Analysis in a sample of 1,892 autistic youth (Mage = 10.82, SDage = 4.14; 420 females), this study aimed to identify subgroups based on the RU and UI profiles. Three profiles of autistic individuals were identified. They were characterized as Low CI, Predominantly RI, and Predominantly UI. Importantly, profiles differed on several key demographic and clinical variables, including age, sex composition, IQ, language level, social and communication abilities, anxiety, and obsessive-compulsive behaviors. Although replication across other samples is needed, the profiles identified in this study are potentially promising for future research given their distinct profiles of RI and UI and unique patterns of associations with key cognitive and clinical variables. Therefore, this study represents an important initial step towards more individualized assessment and support for diverse presentations of CI in autistic youth

Brief Report: A Cross-Sectional Study of Anxiety Levels and Concerns of Chinese Families of Children With Special Educational Needs and Disabilities Post-first-wave of COVID-19

The COVID-19 pandemic has a multifaceted impact on mental health due to ill health, restrictions and lockdowns, and loss of employment and institutional support. COVID-19 may disproportionally impact families with special educational needs and disabilities (SEND) due to the already higher prevalence of mental health conditions in children with SEND and their parents. Therefore, it is essential to determine the short-term impact of the pandemic on the mental health of families with SEND in order to identify their ongoing health support needs. The current study aims to examine the anxiety level and concerns of children with SEND and their parents living in China. The sample consisted of 271 parents of children with SEND aged between 6 and 17 years (M age = 8.37; SD age = 2.76). Parents completed an online survey between 10 April to 8 June 2020. Both child and parental anxiety levels and various concerns increased after the initial wave of COVID-19 when compared with retrospective pre-COVID-19 levels. Parental anxiety and concern levels were significantly higher for those living in rural areas compared to urban areas. In addition, parental and child anxiety and concern levels were significantly correlated with each other. Parental anxiety at the lowest level made a unique and significant statistical contribution to children's anxiety levels. The implications of the study findings are discussed