Regular Neighborhood Research Articles

Vector bundle automorphisms preserving Morse-Bott foliations

Let M be a smooth manifold and F a Morse-Bott foliation with a compact critical manifold Σ⊂M. Denote by D(F) the group of diffeomorphisms of M leaving invariant each leaf of F. Under certain assumptions on F it is shown that the computation of the homotopy type of D(F) reduces to three rather independent groups: the group of diffeomorphisms of Σ, the group of vector bundle automorphisms of some regular neighborhood of Σ, and the subgroup of D(F) consisting of diffeomorphisms fixed near Σ. Examples of computations of homotopy types of groups D(F) for such foliations are also presented.

Hippodamus of Miletus: The shield of the city and the fabric of history

One of the most widespread urban planning systems in European culture is named after Hippodamus of Miletus. The philosophical and religious meanings that were attached to the rectangular grid of streets and geometrically regular neighbourhoods changed over time. In antiquity, this grid was similar to the ancient Greeks’ and Romans’ ideas of the structure of the universe. In the Classical era the meanings were shaped by the philosophy of rationalism. In the early twentieth century the Hippodamean system was seen as rational, functional and democratic, which corresponded to the philosophy of life of that time. The meaning of the Hippodamean system can be revealed by means of the metaphor of weaving and the archetypes of shield and fabric.

Neutrosophic Soft Regular Semiopen Sets in Neutrosophic Soft Topological Spaces

In this paper, we introduce and study the concept of neutrosophic soft regular semiopen and neutrosophic soft regular semiclosed sets in neutrosophic soft topological spaces. By using neutrosophic soft regular semiopen set, we define a new neutrosophic soft interior operator namely neutrosophic soft regular semi interior operator and neutrosophic soft regular semi neighborhood. Also the relation between these sets and counter examples for the reverse relation are given.

Computing a Link Diagram From Its Exterior

A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by planar diagrams, whereas their exteriors, which are compact 3-manifolds with torus boundary, are encoded by triangulations. Here, we give the first practical algorithm for finding a diagram of a knot given a triangulation of its exterior. Our method applies to links as well as knots, and allows us to recover links with hundreds of crossings. We use it to find the first diagrams known for 23 principal congruence arithmetic link exteriors; the largest has over 2500 crossings. Other applications include finding pairs of knots with the same 0-surgery, which relates to questions about slice knots and the smooth 4D Poincaré conjecture.

Infinite presentations for fundamental groups of surfaces

For any finite type connected surface S, we give an infinite presentation of the fundamental group π1(S,*) of S based at an interior point *∈S whose generators are represented by simple loops. When S is non-orientable, we also give an infinite presentation of the subgroup of π1(S,*) generated by elements which are represented by simple loops whose regular neighborhoods are annuli.

Incremental Dictionary Learning-Driven Tensor Low-Rank and Sparse Representation for Hyperspectral Image Classification

Low-rank and sparse representation (LRSR) has gained popularity in hyperspectral image (HSI) classification. However, existing LRSR models usually treat HSI as a two-dimensional matrix, which may destroy the original 3D intrinsic structure of HSI. Moreover, the dictionary consisting of only training samples lacks completeness and may be suboptimal for representation. To overcome the above issues, we propose an incremental dictionary learning-driven tensor low-rank and sparse representation (TLRSR-IDL) model for HSI classification. First, we represent HSI as a third-order tensor to retain its original 3D intrinsic structure by using the TLRSR model, which also combines both sparsity and low rankness to maintain global and local data structures. Second, we design an optimal reconstruction within regularized neighborhood (ORRN) method to exploit spectral-spatial information by avoiding the interference of heterogeneous samples in the neighborhood. Finally, an incremental dictionary learning (IDL) scheme is designed to iteratively introduce augmented samples into the dictionary, and the final classification map is produced by feeding back the last round of the incremental dictionary into the TLRSR-IDL model. The main innovative contribution lies in that the proposed IDL scheme can leverage supervised and unsupervised information, which greatly enhances traditional LRSR and TLRSR models. Experimental results based on three popular hyperspectral datasets demonstrate that the proposed method outperforms other related counterparts in terms of classification accuracy and generalization performance, with OA improvements of 0.97%-16.83%, 1.25%-6.89%, and 0.85%-6.67% for Indian Pines, Pavia University, and Salinas, respectively.

Clinical and psychosocial profile of persons with mental illness living in non-hospital residential facilities in a district in Kerala, India: A cross-sectional survey.

Clinical and psychosocial profiles of persons living with mental illness (PMI) in non-hospital settings in India have not been adequately studied. This study describes the profile of PMI living in non-hospital settings by focussing on variables like functioning and social networks. Residents of all available residential facilities in one district area were surveyed and descriptive data was obtained. Socio occupational functioning was assessed using the Social and Occupational Functioning Scale (SOFS) and social network was measured by modified Lubben Social Network Scale-6 (LSNS-6). A total of nine centres housing 491 residents (7-128) were surveyed via field visits. The mean age of the residents was 49 ± 14.0 years. Fifty per cent of them were never married, 22% were separated or widowed. Almost half of the people had psychotic disorders, while diagnosis could not be delineated in a quarter of the population. Almost half the people reached the facilities with the help of their families, while 40% were brought by police or volunteers who found them wandering. Impairment in socio-occupational functioning was only mild in 90% of residents, while 60% did not contact relatives or friends in the past 3 months. PMI living in non-hospital residential facilities were on average in their middle age and were deficient in marital bonds and other social support. They had reached the centres with the help of extended family or by police/volunteers who rescued them from wandering status. Nevertheless, most of them had only mild to moderate levels of impairment, and their functional capacity was good for independent living in the community with support. Hence, newer models of supported housing that provide greater community reintegration, like independent shared housing within regular neighbourhoods, can be tried. In persons with residual family ties, providing continuous community-based support may help re-establish family integration.

Manifold Neighbourhoods and a Conjecture of Adjamagbo

We verify a conjecture of P. Adjamagbo that if the frontier of a relatively compact subset $V_0$ of a manifold is a submanifold then there is an increasing family $\{V_r\}$ of relatively compact open sets indexed by the positive reals so that the frontier of each is a submanifold, their union is the whole manifold and for each $r\ge 0$ the subfamily indexed by $(r,\infty)$ is a neighbourhood basis of the closure of the $r^{\rm th}$ set. We use smooth collars in the differential category, regular neighbourhoods in the piecewise linear category and handlebodies in the topological category.

Simple embeddings of rational homology balls and antiflips

Let $V$ be a regular neighborhood of a negative chain of $2$-spheres (i.e. exceptional divisor of a cyclic quotient singularity), and let $B_{p,q}$ be a rational homology ball which is smoothly embedded in $V$. Assume that the embedding is simple, i.e. the corresponding rational blow-up can be obtained by just a sequence of ordinary blow-ups from $V$. Then we show that this simple embedding comes from the semi-stable minimal model program (MMP) for $3$-dimensional complex algebraic varieties under certain mild conditions. That is, one can find all simply embedded $B_{p,q}$'s in $V$ via a finite sequence of antiflips applied to a trivial family over a disk. As applications, simple embeddings are impossible for chains of $2$-spheres with self-intersections equal to $-2$. We also show that there are (infinitely many) pairs of disjoint $B_{p,q}$'s smoothly embedded in regular neighborhoods of (almost all) negative chains of $2$-spheres. Along the way, we describe how MMP gives (infinitely many) pairs of disjoint rational homology balls $B_{p,q}$ embedded in blown-up rational homology balls $B_{n,a} # \bar{\mathbb{CP}^2}$ (via certain divisorial contractions), and in the Milnor fibers of certain cyclic quotient surface singularities. This generalizes results in [Khodorovskiy-2014], [H. Park-J. Park-D. Shin-2016], [Owens-2017] by means of a uniform point of view.

The poverty business: landlords, illicit practices and reproduction of disadvantaged neighbourhoods in Czechia

This paper is guided by the question: How do illicit practices of organized groups contribute to the formation and reproduction of disadvantaged neighbourhoods in Czechia? By asking this question we depart from the dominant understanding of disadvantaged neighbourhoods in the study of organized crime. Instead of seeing them as “breeding grounds of organized crime”, it is explored how regular neighbourhoods can decline as a result of illicit practices carried out by certain organized groups. The context of the paper is the so-called “poverty business”, which refers to the renting of overpriced, substandard housing, financed considerably using housing benefits and thus exploiting the housing need of vulnerable social groups, namely Roma. Using the literature on Roma marginalization and illicit housing practices, an analytical framework that consists of the concepts of speculation, exploitation and liquidation is created and applied to two cases of disadvantaged neighbourhoods: “the Hostel” in Brno and “the Neighbourhood” in Litvínov. In conclusion, the adequacy of the organized crime perspective is critically discussed and the need for further research articulated.

Regularity in Topological Modules

The framework of Functional Analysis is the theory of topological vector spaces over the real or complex field. The natural generalization of these objects are the topological modules over topological rings. Weakening the classical Functional Analysis results towards the scope of topological modules is a relatively new trend that has enriched the literature of Functional Analysis with deeper classical results as well as with pathological phenomena. Following this trend, it has been recently proved that every real or complex Hausdorff locally convex topological vector space with dimension greater than or equal to 2 has a balanced and absorbing subset with empty interior. Here we propose an extension of this result to topological modules over topological rings. A sufficient condition is provided to accomplish this extension. This sufficient condition is a new property in topological module theory called strong open property. On the other hand, topological regularity of closed balls and open balls in real or complex normed spaces is a trivial fact. Sufficient conditions, related to the strong open property, are provided on seminormed modules over an absolutely semivalued ring for closed balls to be regular closed and open balls to be regular open. These sufficient conditions are in fact characterizations when the seminormed module is the absolutely semivalued ring. These characterizations allow the provision of more examples of closed-unit neighborhoods of zero. Consequently, the closed-unit ball of any unital real Banach algebra is proved to be a closed-unit zero-neighborhood. We finally transport all these results to topological modules over topological rings to obtain nontrivial regular closed and regular open neighborhoods of zero. In particular, if M is a topological R-module and m∗∈M∗ is a continuous linear functional on M which is open as a map between topological spaces, then m∗−1(int(B)) is regular open and m∗−1(B) is regular closed, for B any closed-unit zero-neighborhood in R.

Rotation Numbers and the Euler Class in Open Books

This paper introduces techniques for computing a variety of numerical invariants associated with a Legendrian knot in a contact manifold presented by an open book with a Morse structure. Such a Legendrian knot admits a front projection to the boundary of a regular neighborhood of the binding. From this front projection, we compute the rotation number for any null-homologous Legendrian knot as a count of oriented cusps and linking or intersection numbers; in the case that the manifold has nontrivial second homology, we can recover the rotation number with respect to a Seifert surface in any homology class. We also provide explicit formulas for computing the necessary intersection numbers from the front projection, and we compute the Euler class of the contact structure supported by the open book. Finally, we introduce a notion of Lagrangian projection and compute the classical invariants of a null-homologous Legendrian knot from its projection to a fixed page.

Characteristics of supported living – a perspective of professionals and potential residents

Abstract Background Policies are increasingly decentralized, and people with a demand for support often live in familiar environments and regular neighborhoods instead of institutions. To meet the demand for support, the local government aims to offer supported living facilities in Staphorst, Netherlands. Accordingly, this study aimed to provide insight into the characteristics of supported living from the perspective of professionals and potential residents. Methods Semi-structured interviews were conducted with professionals and potential residents to obtain insight about their perspectives regarding supported living. First, ten interviews were conducted with professionals (i.e. local government, care, welfare, and housing corporation), followed by six interviews with potential residents and/or their parents. The interviews were transcribed, coded and analyzed by two researchers. Results A small amount of the residents in Staphorst would benefit from supported living. This concerns mainly (young) adults with a mild intellectual disability and/or a mental illness who need practical, social and emotional support in order to live on their own. Composing the support, it is important to acknowledge the religious identity of the potential residents and their families. Furthermore, the interviews with professionals and potential residents revealed that the following options should be considered: time-out, short- and long-term support, daycare and open house facilities, various types of support (i.e. volunteer and professional) and combining target groups (i.e. adolescents and adults). Conclusions This study reveals several options to consider when composing supported living in Staphorst. Accordingly, most participants emphasized the need for short-term support focusing on skills related to independent living. Furthermore, it is important to involve professionals and potential residents and/or their parents in order to offer sustainable supported living for the residents in Staphorst. Key messages Most participants emphasized the need for short-term support focusing on skills related to independent living. Both professionals and potential residents should be involved when composing supported living facilities.

On tunnel numbers of a cable knot and its companion

Let K be a nontrivial knot in S3 and t(K) its tunnel number. For any (p≥2,q)-slope in the torus boundary of a closed regular neighborhood of K in S3, denoted by K⋆, it is a nontrivial cable knot in S3. Though t(K⋆)≤t(K)+1, Example 1.1 in Section 1 shows that in some case, t(K⋆)≤t(K). So it is interesting to know when t(K⋆)=t(K)+1.After using some combinatorial techniques, we prove that (1) for any nontrivial cable knot K⋆ and its companion K, t(K⋆)≥t(K); (2) if either K admits a high distance Heegaard splitting or p/q is far away from a fixed subset in the Farey graph, then t(K⋆)=t(K)+1. Using the second conclusion, we construct a satellite knot and its companion so that the difference between their tunnel numbers is arbitrary large.

Assessment of Availability and Use of Teaching and Learning Resources for Retention of Learners with Special Needs in Regular Primary Schools in Dadaab Sub-County, Kenya

The status of implementation of inclusive education in terms of availability and use of teaching and learning resources for retention of learners with special needs in Garissa County was unknown. Inclusive education refers to a situation where learners with disabilities and special educational needs have full membership in age-appropriate classes in their regular neighborhood schools with appropriate supplementary aids and support services. Records from Educational Assessment and Resource Centres (EARC) Garissa County revealed that there was a decline in the retention rate of learners` admitted. For example, in the year 2014, the retention rate was 37 learners (45.7%), 2015 (114 learners, 38.0%), 2016 (43 learners, 28.9%), 2017 (35 learners, 31.5%) and 2018 (41 learners, 23.7%). The purpose of the study was to assess the status of implementation of inclusive education practices for the retention of learners with special needs in regular primary schools in Dadaab sub-county. The specific objective of the study was to establish the extent to which the availability and use of teaching and learning resources affect the retention of learners with special needs in regular primary schools in Dadaab sub-county. The study adopted a descriptive survey research design. The target population comprised 26 head-teachers, 78 teachers, 300 learners with special needs, and 4 education officers. Saturated sampling technique was used to select 23 head-teachers, 70 teachers, 100 learners with special needs, and 4 education officers. Instruments for data collection were questionnaires, interview schedules and observation schedules. Quantitative data were analyzed using frequency counts, percentages, and mean. The findings of the study indicated that the availability and use of teaching and learning materials were inadequate (mean= 2.18). The study concluded that the low retention of learners with special needs as a result of the availability and use of teaching and learning materials to a small extent. The study recommended that the country and national government should ensure that there is adequate provision of teaching and learning resources to enhance learning for learners with special needs. The budget for materials should be enhanced. The study also recommends to non-governmental organizations to assist regular primary schools to access teaching and learning materials that can be used by learners with special needs.

CS4Some? Differences in Technology Learning Readiness

This article investigates the extent to which teens are ready to take advantage of the Computer Science for All (CS4All) initiative promoted in 2016 by the Obama administration. Using new survey data from a socioeconomically stratified random sample of eighth graders in regular neighborhood schools in Chicago, author Cassidy Puckett looks at differences in students' technology learning readiness, operationalized as the use of five technology learning habits, and home and school resources and practices that explain these differences. Findings show that students vary in their technology learning readiness, which suggests the need for intervention before high school, and that families shape readiness, but schools largely do not. This study contributes to debates about schools' relationship to inequality by identifying a mechanism through which policies can inadvertently exacerbate inequities without understanding and addressing readiness; it also offers possible methods for interventions in schools.

Neighborhood equivalence for multibranched surfaces in 3-manifolds

A multibranched surface is a 2-dimensional polyhedron without vertices. We introduce moves for multibranched surfaces embedded in a 3-manifold, which connect any two multibranched surfaces with the same regular neighborhoods in finitely many steps.

Regular neighbourhoods and canonical decompositions for groups

Regular neighbourhoods and canonical decompositions for groups

PENGARUH KOMUNIKASI ANTARPRIBADI TERHADAP KONSEP DIRI JULIANTO EKA PUTRA

Success is not only desired and owned by people who are able, but those who cannot afford,even want to have it. For someone who is born from unrich people, having success thing is a pricelesshappiness. It is felt by Julianto Eka Putra who is growing in a regular neighborhood. Julianto EkaPutra initiated and motivated to make the VISION 2010 program with the aim is to establish freeschool and a charitable foundation that dedicated himself to help orphans in Indonesia who cannotafford to continue their study to high school education. The purpose of this study is to determine theeffect of Julianto Eka Putra’s self-concept on the students of Selamat Pagi Indonesia’s High SchoolBatu-Malang. The result of the first hypothesis reads the suspect classification and purpose of theinterpersonal communication affects the self-concept, is acceptable because of the calculation it tcount (1,944) > t table (1,667), second hypothesis is assumed to be accepted because of theeffectiveness of interpersonal communication is known that t count (4,335) > t table (1,667), thismeans that the independent variable X1 (classification and interpersonal communication objective)and X2 (interpersonal communication effectiveness) significantly affects the self concept of JuliantoEka Putra.Keywords: Classification and Interpersonal Communication Objective, Interpersonal CommunicationEffectiveness, Self Concept

The Price of Dependence.

The Price of Dependence Keynan Hobbs In the early 1990's I was signing out of Ft. Campbell, KY, and there was a person sitting at a small folding table just a few feet before door that led off the base and to where I was going next. I was at the end of my time with the 502nd Infantry, 101st Airborne Division, nine months back from combat in Desert Storm, and at the end of my enlistment. I walked up to the folding table, already kind of looking past it, and the person there asked me about any health problems I'd had while I was in the Army—anything that ached, pained, any injuries, anything I'd been treated for by Army medical personnel. I told him whatever I could recall, thinking that this was some sort of requirement before getting the hell out of there. Months later, back at home, I started getting letters with appointments scheduled at the nearest VA Medical Center. What I had done at that folding table, it turned out, was file a claim for service-connected disability compensation for all of the ailments I could think of, and now I was to be examined by VA clinicians. I had no idea that it was the start of my relationship with VA benefits and healthcare. [End Page 80] For a long time while I was working entry-level jobs and studying in college, I had no other option for healthcare than VA. I appreciated it, and hated it too. I take that back—I didn't really appreciate it much. It was dismal, and depressing. I hated going to the facilities, because they were filled with things that reminded me of what I was trying to forget. Drab hallways were filled with military crests and photographs of old battles on the walls, lines to wait in so that I could be placed into other lines. Inevitably thoughts about combat, the friends I hadn't seen in years, and how much I missed both the simplicity and terror of when deployment would start. And that was just getting to the waiting area. Inside the clinics there was little privacy. Eventually, a physician would come in and review my symptoms. The eight or so medical students standing behind him would nod and peer over his shoulder and take notes, while he examined and palpated and tested my range of motion. When he was done, it was the medical students' turn. It seemed like I was prescribed Naproxen for everything. Literally everything. I'm sure that wasn't really the case, but I know that the treatment options presented to me were so few that I quit going. What was the point, unless I really, really needed more Naproxen? I very rarely used any kind of healthcare for years after I stopped using VA. I was hit by a car on my bicycle, and refused the ambulance ride because I was afraid of what it would cost. I realized that I really was injured later though, and went to the nearest VA hospital. I was treated for a badly bruised hip, and received a prostate exam from a medical student. I'm not kidding, a prostate exam. I learned something fundamental about VA Healthcare from that experience: you don't get something for nothing. The best experience that I ever had with VA healthcare, and it was truly the one I needed most, was my care at the Vet Center for "readjustment counseling." I had reached a point where post-traumatic stress was starting to pour out of the seams of the life I was holding together, and a college counselor referred me to the Vet Center for help. The Vet Center wasn't like the regular VA facilities—it had familiar military stuff in the waiting room, but it was also in an old house in a regular neighborhood. And everyone there, clinicians and administrators, related to me as a human being first. I never felt reduced to an example of my disorder, or an inconvenience. A few years after my therapy there, I changed careers and went back to college in order to become...