Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

A Characterization of Weakly Lindelöf Determined Banach Spaces

2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

Upper and Lower Bounds in Relator Spaces

2000 Mathematics Subject Classification: 06A06, 54E15

Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces

2000 Mathematics Subject Classification: 47H10, 54E15.

Distance Distributions and Energy of Designs in Hamming Spaces

We obtain new combinatorial upper and lower bounds for the potential energy of designs in q-ary Hamming space. Combined with results on reducing the number of all feasible distance distributions of such designs this gives reasonable good bounds. We compute and compare our lower bounds to recently obtained universal lower bounds. Some examples in the binary case are considered.

Automatized Generation of Personalized Learning Paths through Aspects in Multidimensional Spaces

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Law Enforcement Actions in Urban Spaces Governed by Violent Non-State Entities: Lessons from Latin America

In response to a crime epidemic afflicting Latin America since the early 1990s, several countries in the region have resorted to using heavy-force police or military units to physically retake territories de facto controlled by non-State criminal or insurgent groups. After a period of territory control, the heavy forces hand law enforcement functions in the retaken territories to regular police officers, with the hope that the territories and their populations will remain under the control of the state. To a varying degree, intensity, and consistency, Brazil, Colombia, Mexico, and Jamaica have adopted such policies since the mid-1990s. During such operations, governments need to pursue two interrelated objectives: to better establish the state’s physical presence and to realign the allegiance of the population in those areas toward the state and away from the non-State criminal entities. From the perspective of law enforcement, such operations entail several critical decisions and junctions, such as: Whether or not to announce the force insertion in advance. The decision trades off the element of surprise and the ability to capture key leaders of the criminal organizations against the ability to minimize civilian casualties and force levels. The latter, however, may allow criminals to go to ground and escape capture. Governments thus must decide whether they merely seek to displace criminal groups to other areas or maximize their decapitation capacity. Intelligence flows rarely come from the population. Often, rival criminal groups are the best source of intelligence. However, cooperation between the State and such groups that goes beyond using vetted intelligence provided by the groups, such as a State tolerance for militias, compromises the rule-of-law integrity of the State and ultimately can eviscerate even public safety gains. Sustaining security after initial clearing operations is at times even more challenging than conducting the initial operations. Although unlike the heavy forces, traditional police forces, especially if designed as community police, have the capacity to develop trust of the community and ultimately focus on crime prevention, developing such trust often takes a long time. To develop the community’s trust, regular police forces need to conduct frequent on-foot patrols with intensive nonthreatening interactions with the population and minimize the use of force. Moreover, sufficiently robust patrol units need to be placed in designated beats for substantial amount of time, often at least over a year. Establishing oversight mechanisms, including joint police-citizens’ boards, further facilities building trust in the police among the community. After disruption of the established criminal order, street crime often significantly rises and both the heavy-force and community-police units often struggle to contain it. The increase in street crime alienates the population of the retaken territory from the State. Thus developing a capacity to address street crime is critical. Moreover, the community police units tend to be vulnerable (especially initially) to efforts by displaced criminals to reoccupy the cleared territories. Losing a cleared territory back to criminal groups is extremely costly in terms of losing any established trust and being able to recover it. Rather than operating on a priori determined handover schedule, a careful assessment of the relative strength of regular police and criminal groups post-clearing operations is likely to be a better guide for timing the handover from heavy forces to regular police units. Cleared territories often experience not only a peace dividend, but also a peace deficit – in the rise new serious crime (in addition to street crime). Newly – valuable land and other previously-inaccessible resources can lead to land speculation and forced displacement; various other forms of new crime can also significantly rise. Community police forces often struggle to cope with such crime, especially as it is frequently linked to legal business. Such new crime often receives little to no attention in the design of the operations to retake territories from criminal groups. But without developing an effective response to such new crime, the public safety gains of the clearing operations can be altogether lost.

DiCER: A distributed consumer experience research method for use in public spaces

Date of Acceptance: 06/03/2015 Acknowledgement: This research was funded by NCR and the Northern Research Partnership

DiCER: A distributed consumer experience research method for use in public spaces

Date of Acceptance: 06/03/2015 Acknowledgement: This research was funded by NCR and the Northern Research Partnership

DiCER: A distributed consumer experience research method for use in public spaces

Date of Acceptance: 06/03/2015 Acknowledgement: This research was funded by NCR and the Northern Research Partnership

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Differential activation in temporal, cingulate and prefrontal cortices during response inhibition in bipolar disorder

Background: Increased impulsivity and aberrant response inhibition have been observed in bipolar disorder (BD). This study examined the functional abnormalities and underlying neural processes during response inhibition in BD, and its relationship to impulsivity. Methods: We assessed impulsivity using the Barratt Impulsiveness Scale (BIS) and, using functional magnetic resonance imaging (fMRI), measured neural activity in response to an Affective Go-NoGo Task, consisting of emotional facial stimuli (fear, happy, anger faces) and non-emotional control stimuli (neutral female and male faces) in euthymic BD (n=23) and healthy individuals (HI; n=25). Results: BD patients were significantly more impulsive, yet did not differ from HI on accuracy or reaction time on the emotional go/no-go task. Comparing neural patterns of activation when processing emotional Go versus emotional NoGo trials yielded increased activation in BD within temporal and cingulate cortices and within prefrontal-cortical regions in HI. Furthermore, higher BIS scores for BD were associated with slower reaction times, and indicative of compensatory cognitive strategies to counter increased impulsivity. Conclusions: These findings illustrate cognition-emotion interference in BD and the observed differences in neural activation indicate potentially altered emotion modulation. Increased activation in brain regions previously shown in emotion regulation and response inhibition tasks could represent a disease-specific marker for BD

Shared Education in contested spaces: How collaborative networks improve communities and schools

Societies which suffer from ethnic and political divisions are often characterised by patterns of social and institutional separation, and sometimes these divisions remain even after political conflict has ended. This has occurred in Northern Ireland where there is, and remains, a long-standing pattern of parallel institutions and services for the different communities. A socially significant example lies in the education system where a parallel system of Catholic and Protestant schools has been in place since the establishment of a national school system in the 1830s. During the years of political violence in Northern Ireland a variety of educational interventions were implemented to promote reconciliation, but most of them failed to create any systemic change. This paper describes a post-conflict educational initiative known as Shared Education which aims to promote social cohesion and school improvement by encouraging sustained and regular shared learning between students and broader collaboration between teachers and school leaders from different schools. The paper examines the background to work on Shared Education, describes a ‘sharing continuum’ which emerged as an evaluation and policy tool from this work and considers evidence from a case study of a Shared Education school partnership in a divided city in Northern Ireland. The paper will conclude by highlighting some of the significant social and policy impact of the Shared Education work.