A functional central limit theorem for a Markov-modulated infinite-server queue

The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under specific time-scaling; the background process is sped up by $N^{\alpha}$, the arrival rates are scaled by $N$, for $N$ large. A functional central limit theorem is derived for $M$, which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on $\alpha$ is observed. For $\alpha\leq1$ the parameters of the limiting process contain the deviation matrix associated with the background process.Comment: 4 figure

The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries

Proactive multi-tenant cache management for virtualized ISP networks

The content delivery market has mainly been dominated by large Content Delivery Networks (CDNs) such as Akamai and Limelight. However, CDN traffic exerts a lot of pressure on Internet Service Provider (ISP) networks. Recently, ISPs have begun deploying so-called Telco CDNs, which have many advantages, such as reduced ISP network bandwidth utilization and improved Quality of Service (QoS) by bringing content closer to the end-user. Virtualization of storage and networking resources can enable the ISP to simultaneously lease its Telco CDN infrastructure to multiple third parties, opening up new business models and revenue streams. In this paper, we propose a proactive cache management system for ISP-operated multi-tenant Telco CDNs. The associated algorithm optimizes content placement and server selection across tenants and users, based on predicted content popularity and the geographical distribution of requests. Based on a Video-on-Demand (VoD) request trace of a leading European telecom operator, the presented algorithm is shown to reduce bandwidth usage by 17% compared to the traditional Least Recently Used (LRU) caching strategy, both inside the network and on the ingress links, while at the same time offering enhanced load balancing capabilities. Increasing the prediction accuracy is shown to have the potential to further improve bandwidth efficiency by up to 79%

Towards multi-tenant cache management for ISP networks

The decreasing cost of storage and the advent of virtualization technology can allow Internet Service Providers (ISPs) to deploy multi-tenant caching infrastructures and lease them to content producers and Content Delivery Networks (CDNs). Serving content requests directly from the ISP network does not only reduce the delivery time, but also allows the ISP to optimize the network resources by controlling the placement and routing of content items. In this paper, we introduce a multi-tenant cache management approach that significantly reduces the bandwidth utilization of ISPs networks by pro-actively allocating caching space, leased by content producers and/or CDNs, and intelligently routing content to the end users. Using real content request traces, we show that the optimal solution to this problem can increase the cache hit ratio by 70.64% while reducing the bandwidth usage by 57.17% on average, compared to a commonly used reactive cache management scheme. These results provide a benchmark for the development of novel multi-tenant cache management strategies

Towards multi-tenant cache management for ISP networks

The decreasing cost of storage and the advent of virtualization technology can allow Internet Service Providers (ISPs) to deploy multi-tenant caching infrastructures and lease them to content producers and Content Delivery Networks (CDNs). Serving content requests directly from the ISP network does not only reduce the delivery time, but also allows the ISP to optimize the network resources by controlling the placement and routing of content items. In this paper, we introduce a multitenant cache management approach that significantly reduces the bandwidth utilization of ISPs networks by pro-actively allocating caching space, leased by content producers and/or CDNs, and intelligently routing content to the end users. Using real content request traces, we show that the optimal solution to this problem can increase the cache hit ratio by 70.64% while reducing the bandwidth usage by 57.17% on average, compared to a commonly used reactive cache management scheme. These results provide a benchmark for the development of novel multi-tenant cache management strategies

Plasma fibrinogen: now also an antidepressant response marker?

Major depressive disorder (MDD) is one of the leading causes of global disability. It is a risk factor for noncompliance with medical treatment, with about 40% of patients not responding to currently used antidepressant drugs. The identification and clinical implementation of biomarkers that can indicate the likelihood of treatment response are needed in order to predict which patients will benefit from an antidepressant drug. While analyzing the blood plasma proteome collected from MDD patients before the initiation of antidepressant medication, we observed different fibrinogen alpha (FGA) levels between drug responders and nonresponders. These results were replicated in a second set of patients. Our findings lend further support to a recently identified association between MDD and fibrinogen levels from a large-scale study

S^1 \times S^2 as a bag membrane and its Einstein-Weyl geometry

In the hybrid skyrmion in which an Anti-de Sitter bag is imbedded into the skyrmion configuration a S^{1}\times S^{2} membrane is lying on the compactified spatial infinity of the bag [H. Rosu, Nuovo Cimento B 108, 313 (1993)]. The connection between the quark degrees of freedom and the mesonic ones is made through the membrane, in a way that should still be clarified from the standpoint of general relativity and topology. The S^1 \times S^2 membrane as a 3-dimensional manifold is at the same time a Weyl-Einstein space. We make here an excursion through the mathematical body of knowledge in the differential geometry and topology of these spaces which is expected to be useful for hadronic membranesComment: 9pp in latex, minor correction

Topologically Massive Gravity and Ricci-Cotton Flow

We consider Topologically Massive Gravity (TMG), which is three dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly

Proactive Multi-tenant Cache Management for Virtualized ISP Networks

The content delivery market has mainly been dominated by large Content Delivery Networks (CDNs) such as Akamai and Limelight. However, CDN traffic exerts a lot of pressure on Internet Service Provider (ISP) networks. Recently, ISPs have begun deploying so-called Telco CDNs, which have many advantages, such as reduced ISP network bandwidth utilization and improved Quality of Service (QoS) by bringing content closer to the end-user. Virtualization of storage and networking resources can enable the ISP to simultaneously lease its Telco CDN infrastructure to multiple third parties, opening up new business models and revenue streams. In this paper, we propose a proactive cache management system for ISP-operated multitenant Telco CDNs. The associated algorithm optimizes content placement and server selection across tenants and users, based on predicted content popularity and the geographical distribution of requests. Based on a Video-on-Demand (VoD) request trace of a leading European telecom operator, the presented algorithm is shown to reduce bandwidth usage by 17% compared to the traditional Least Recently Used (LRU) caching strategy, both inside the network and on the ingress links, while at the same time offering enhanced load balancing capabilities. Increasing the prediction accuracy is shown to have the potential to further improve bandwidth efficiency by up to 79%

Scalable Cache Management for ISP-Operated Content Delivery Services

Content delivery networks (CDNs) have been the prevalent method for the efficient delivery of content across the Internet. Management operations performed by CDNs are usually applied only based on limited information about Internet Service Provider (ISP) networks, which can have a negative impact on the utilization of ISP resources. To overcome these issues, previous research efforts have been investigating ISP-operated content delivery services, by which an ISP can deploy its own in-network caching infrastructure and implement its own cache management strategies. In this paper, we extend our previous work on ISP-operated content distribution and develop a novel scalable and efficient distributed approach to control the placement of content in the available caching points. The proposed approach relies on parallelizing the decision-making process and the use of network partitioning to cluster the distributed decision-making points, which enables fast reconfiguration and limits the volume of information required to take reconfiguration decisions. We evaluate the performance of our approach based on a wide range of parameters. The results demonstrate that the proposed solution can outperform previous approaches in terms of management overhead and complexity while offering similar network and caching performance