On the KNS Conjecture in type EE

For the exceptional types $E_6$, $E_7$, and $E_8$, we prove that the specializations at roots of unity of the quantum dimensions of the Kirillov-Reshetikhin modules give real solutions of $\ell$-restricted $Q$-systems, as conjectured by Kuniba, Nakanishi, and Suzuki. We also show that these solutions are positive in type $E_6$. In type $E_7$ and $E_8$, we only prove positivity for a subset of the nodes of the Dynkin diagram.Comment: 28 pages, 1 figur

Quantum affine algebras at roots of unity and generalised cluster algebras

Let $U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_2)$ be the restricted integral form of the quantum loop algebra $U_q(L\mathfrak{sl}_2)$ specialised at a root of unity $\varepsilon$. We prove that the Grothendieck ring of a tensor subcategory of representations of $U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_2)$ is a generalised cluster algebra of type $C_{l-1}$, where $l$ is the order of $\varepsilon^2$. Moreover, we show that the classes of simple objects in the Grothendieck ring essentially coincide with the cluster monomials. We also state a conjecture for $U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_3)$, and we prove it for $l=2$.Comment: 26 pages, 9 figure

Generalised cluster algebras and qq-characters at roots of unity

International audienceShapiro and Chekhov (2011) have introduced the notion of generalised cluster algebra; we focus on an example in type $C_n$. On the other hand, Chari and Pressley (1997), as well as Frenkel and Mukhin (2002), have studied the restricted integral form $U^{\mathtt{res}}_ε (\widehat{\mathfrak{g}})$ of a quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ where $q=ε$ is a root of unity. Our main result states that the Grothendieck ring of a tensor subcategory $C_{ε^\mathbb{z}}$ of representations of $U^{\mathtt{res}}_ε (L\mathfrak{sl}_2)$ is a generalised cluster algebra of type $C_{l−1}$, where $l$ is the order of $ε^2$. We also state a conjecture for $U^{\mathtt{res}}_ε (L\mathfrak{sl}_3)$, and sketch a proof for $l=2$.Shapiro et Chekhov (2011) ont introduit la notion d'algèbre amassée généralisée; nous étudions un exemple en type $C_n$. Par ailleurs, Chari et Pressley (1997), ainsi que Frenkel et Mukhin (2002), ont étudié la forme entière restreinte $U^{\mathtt{res}}_ε (\widehat{\mathfrak{g}})$ d'une algèbre affine quantique $U_q(\widehat{\mathfrak{g}})$ où $q=ε$ est une racine de l'unité. Notre résultat principal affirme que l'anneau de Grothendieck d'une sous-catégorie tensorielle $C_{ε^\mathbb{z}}$ de représentations de $U^{\mathtt{res}}_ε (L\mathfrak{sl}_2)$ est une algèbre amassée généralisée de type $C_{l−1}$, où $l$ est l'ordre de $ε^2$. Nous conjecturons une propriété similaire pour $U^{\mathtt{res}}_ε (L\mathfrak{sl}_3)$ et donnons un aperçu de la preuve pour $l=2$

Transient Addressing for Related Processes: Improved Firewalling by Using IPV6 and Multiple Addresses per Host

Traditionally, hosts have tended to assign relatively few network addresses to an interface for extended periods. Encouraged by the new abundance of addressing possibilities provided by IPv6, we propose a new method, called Transient Addressing for Related Processes (TARP), whereby hosts temporarily employ and subsequently discard IPv6 addresses in servicing a client host's network requests. The method provides certain security advantages and neatly finesses some well-known firewall problems caused by dynamic port negotiation used in a variety of application protocols. A prototype implementation exists as a small set of kame/BSD kernel enhancements and allows socket programmers and applications nearly transparent access to TARP addressing's advantages

Generalised cluster algebras and qq-characters at roots of unity

Shapiro and Chekhov (2011) have introduced the notion of generalised cluster algebra; we focus on an example in type $C_n$. On the other hand, Chari and Pressley (1997), as well as Frenkel and Mukhin (2002), have studied the restricted integral form $U^{\mathtt{res}}_ε (\widehat{\mathfrak{g}})$ of a quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ where $q=ε$ is a root of unity. Our main result states that the Grothendieck ring of a tensor subcategory $C_{ε^\mathbb{z}}$ of representations of $U^{\mathtt{res}}_ε (L\mathfrak{sl}_2)$ is a generalised cluster algebra of type $C_{l−1}$, where $l$ is the order of $ε^2$. We also state a conjecture for $U^{\mathtt{res}}_ε (L\mathfrak{sl}_3)$, and sketch a proof for $l=2$

Disease burden and direct medical costs of incident adult ADHD:A retrospective longitudinal analysis based on German statutory health insurance claims data

Background. Adult attention-deficit/hyperactivity disorder (aADHD) is still a largely unrecognized psychiatric condition despite its strong impact on individuals' well-being. Here, we describe the healthcare situation of individuals with incident aADHD over 4 years before and 4 years after initial administrative diagnosis. Methods. A retrospective, longitudinal cohort analysis was conducted using German claims data. The InGef database contained approximately 5 million member-records from over 60 nationwide statutory health insurances (SHI). Individuals were indexed upon initial diagnosis of aADHD. Results. Average age at diagnosis of aADHD was 35 years, and 60% of individuals were male. Comorbidities, resource use, and healthcare costs were substantial before initial diagnosis and decreased within the 4 years thereafter. Only 32% of individuals received initial ADHD medication and adherence was low. The majority received psychotherapy. Individuals with initial ADHD medication showed the highest share in comorbidities, physician visits, medication use for comorbidities, psychotherapy, and costs. Overall, healthcare costs were at over euro4,000 per individual within the year of aADHD diagnosis. Conclusions. We conclude that earlier recognition of aADHD could prevent the development and aggravation of comorbid mental illnesses. At the same time, comorbid conditions may have masked ("over-shadowed") aADHD and delayed diagnosis. The burden of disease in aADHD is high, which was noticeable especially among individuals who received initial ADHD-medication, suggesting that psychopharmacological treatment was mainly considered for the most severely ill. We conclude that measures to facilitate access of aADHD patients to clinical experts are required to improve reality of care in the outpatient setting