Legendrian DGA Representations and the Colored Kauffman Polynomial

For any Legendrian knot $K$ in standard contact ${\mathbb R}^3$ we relate counts of ungraded ($1$-graded) representations of the Legendrian contact homology DG-algebra $(\mathcal{A}(K),\partial)$ with the $n$-colored Kauffman polynomial. To do this, we introduce an ungraded $n$-colored ruling polynomial, $R^1_{n,K}(q)$, as a linear combination of reduced ruling polynomials of positive permutation braids and show that (i) $R^1_{n,K}(q)$ arises as a specialization $F_{n,K}(a,q)\big|_{a^{-1}=0}$ of the $n$-colored Kauffman polynomial and (ii) when $q$ is a power of two $R^1_{n,K}(q)$ agrees with the total ungraded representation number, $\operatorname{Rep}_1\big(K, \mathbb{F}_q^n\big)$, which is a normalized count of $n$-dimensional representations of $(\mathcal{A}(K),\partial)$ over the finite field $\mathbb{F}_q$. This complements results from [Leverson C., Rutherford D., Quantum Topol. 11 (2020), 55-118, arXiv:1802.10531] concerning the colored HOMFLY-PT polynomial, $m$-graded representation numbers, and $m$-graded ruling polynomials with $m \neq 1$

Biomolecular resource utilization in elementary cell-free gene circuits

We present a detailed dynamical model of the behavior of transcription-translation circuits in vitro that makes explicit the roles played by essential molecular resources. A set of simple two-gene test circuits operating in a cell-free biochemical 'breadboard' validate this model and highlight the consequences of limited resource availability. In particular, we are able to confirm the existence of biomolecular 'crosstalk' and isolate its individual sources. The implications of crosstalk for biomolecular circuit design and function are discussed

Understanding tensions and identifying clinician agreement on improvements to early-stage chronic kidney disease monitoring in primary care : a qualitative study

Funding This article presents independent research funded by the National Institute for Health Research School for Primary Care Research (NIHR SPCR) (reference:120). JE was also supported by the NIHR Programme Grants for Applied Research programme (Reference: RP-PG-1210-12012). DSL and LL are supported by the NIHR Oxford Biomedical Research CentrePeer reviewedPublisher PD

KLF6 and STAT3 Co-Occupy Regulatory DNA and Functionally Synergize to Promote Axon Growth in CNS Neurons

The failure of axon regeneration in the CNS limits recovery from damage and disease. Members of the KLF family of transcription factors can exert both positive and negative effects on axon regeneration, but the underlying mechanisms are unclear. Here we show that forced expression of KLF6 promotes axon regeneration by corticospinal tract neurons in the injured spinal cord. RNA sequencing identified 454 genes whose expression changed upon forced KLF6 expression in vitro, including sub-networks that were highly enriched for functions relevant to axon extension including cytoskeleton remodeling, lipid synthesis, and bioenergetics. In addition, promoter analysis predicted a functional interaction between KLF6 and a second transcription factor, STAT3, and genome-wide footprinting using ATAC-Seq data confirmed frequent co-occupancy. Co-expression of the two factors yielded a synergistic elevation of neurite growth in vitro. These data clarify the transcriptional control of axon growth and point the way toward novel interventions to promote CNS regeneration

Perspectives of crisis intervention for people diagnosed with 'borderline personality disorder': an integrative review.

What is known on the subject? - People diagnosed with 'BPD' often experience crisis and use services 'BPD' is a controversial diagnosis, and the experience of crisis and crisis intervention is not well understood. What this paper adds to existing knowledge? - People diagnosed with 'BPD' have different experiences of crisis, and using the diagnosis alone as a basis for deciding care and treatment is not appropriate There are many human factors which can influence how professionals deliver care to people diagnosed with 'BPD'. What are the implications for practice? - The education of staff, views on responsibility, team conflicts and access to clinical supervision can have an impact on how care is delivered, and should be addressed by organizations providing crisis care. Access to care often occurs when a person is self-harming or suicidal, but does not address underlying distress. Crisis care should go beyond managing behaviour and address any underlying needs. Abstract: Introduction 'Borderline personality disorder' ('BPD') is associated with frequent use of crisis intervention services. However, no robust evidence base supports specific interventions, and people's experiences are not well understood. Aim: To explore the experiences of stakeholders involved in the crisis care of people diagnosed with 'BPD'. Method: Integrative review with nine databases searched January 2000 to November 2017. The search filtered 3,169 titles and abstracts with 46 full-text articles appraised and included. Results: Four themes were constructed from thematic analysis: crisis as a recurrent multidimensional cycle, variations and dynamics impacting on crisis intervention, impact of interpersonal dynamics and communication on crisis, and balancing decision-making and responsibility in managing crisis. Discussion: Crisis is a multidimensional subjective experience, which also contributes to distress for family carers and professionals. Crisis interventions had limited and subjective benefit. They are influenced by accessibility of services, different understandings of 'BPD' and human dynamics in complex decision-making, and can be experienced as helpful or harmful. Implications for practice Subjectivity of crisis experiences shows limitations of the diagnostic model of 'BPD', emphasizing that interventions should remain person-centred. While thresholds for intervention are often met after self-harm or suicidality, professionals should review approaches to care and support people with underlying distress

All-optical conditional logic with a nonlinear photonic crystal nanocavity

We demonstrate tunable frequency-converted light mediated by a chi-(2) nonlinear photonic crystal nanocavity. The wavelength-scale InP-based cavity supports two closely-spaced localized modes near 1550 nm which are resonantly excited by a 130 fs laser pulse. The cavity is simultaneously irradiated with a non-resonant probe beam, giving rise to rich second-order scattering spectra reflecting nonlinear mixing of the different resonant and non-resonant components. In particular, we highlight the radiation at the sum frequencies of the probe beam and the respective cavity modes. This would be a useful, minimally-invasive monitor of the joint occupancy state of multiple cavities in an integrated optical circuit.Comment: 4 pages, 4 figure