Wittgenstein on Sameness, Necessity and Privacy

The aim of this paper is to examine Wittgenstein"s arguments against the meaningfulness of statements which state the possessive privacy of sensations; and to demonstrate their incorrectness

A new invariant that's a lower bound of LS-category

Let $X$ be a simply connected CW-complex of finite type and $\mathbb{K}$ any field. A first known lower bound of LS-category $cat(X)$ is the Toomer invariant $e_{\mathbb{K}} (X)$ (\cite{Too}). In $1980$'s F\'elix et al. introduced the concept of {\it depth} in algebraic topology and proved the depth theorem: $depth (H_*(\Omega X, \mathbb{K})) \leq cat(X)$. In this paper, we use the Eilenberg-Moore spectral sequence of $X$ to introduce a new numerical invariant, denoted by \textsc{r}(X, \mathbb{K}), and show that it has the same properties as those of $e_{\mathbb{K}} (X)$. When the evaluation map (\cite{FHT88}) is non-trivial and $char(\mathbb{K})\not = 2$, we prove that \textsc{r}(X, \mathbb{K}) interpolates $depth(H_*(\Omega X, \mathbb{K}))$ and $e_{\mathbb{K}} (X)$. Hence, we obtain an improvement of L. Bisiaux theorem (\cite{Bis99}) and then of the depth theorem. Motivated by these results, we associate to any commutative differential graded algebra $(A,d)$, a purely algebraic invariant \textsc{r}(A,d) and, via the theory of minimal models, we relate it with our previous topological results. In particular, if $(\Lambda V,d)$ is a Sullivan minimal algebra such that $d=\sum_{i\geq k}d_i$ and $d_i(V)\subseteq \Lambda ^iV$, a greater lower bound is obtained, namely e_0(\Lambda V, d)\geq \textsc{r}(\Lambda V, d) + (k-2).Comment: 21 page

Journal Staff

Riskanalysverktyget failure mode and effects analysis (FMEA) som analyserar kompo-nenter och signaler är beroende av att designen av fordonets elsystem finns tillgängligt och utförs därför sent i utvecklingsprocessen av elsystem. Detta medför att vissa fel inte analyseras i tid och kanske måste designas bort i efterhand vilket kan leda till ökad sy-stemkomplexitet samt längre och dyrare utvecklingsprocesser.Målet med examensarbetet är att genom en litteraturstudie ta reda på om det finns me-toder eller arbetssätt som gör att Scania tidigt i utvecklingsprocessen av elsystem kan genomföra funktionsanalyser i sitt riskanalysarbete med FMEA samt analysera dessa.Resultatet av detta examensarbete visar att det är möjligt att påbörja FMEA-arbetet tidigt i utvecklingsprocessen av elsystem om ingenjörerna utgår från ett funktionsperspektiv i riskanalysarbetet där de listar och rangordnar de funktioner som tillsammans realiserar en eller flera funktionaliteter samt deras felmoder, feleffekter, feldetektering, allvarlighet, sannolikhet och frekvens. Med hjälp av en FFMEA kan ingenjörerna tidigt i utveck-lingsprocessen av elsystem snabbt och effektivt hantera de identifierade säkerhetskritiska funktionerna.En befintlig funktionalitet på Scania har brutits ned i funktioner och en FFMEA har genomförts på dessa som en demonstration på hur en FFMEA kan genomföras och se ut.The risk analysis tool failure mode and effects analysis (FMEA) that analyzes the com-ponents and signals of a electrical system is design dependent and are therefore per-formed late in the development process of electrical systems. This could lead to that some errors are not analyzed in time and may need to be designed away which can lead to increased system complexity as well as longer and more expensive development proc-esses.The objective of this study is that through a literature review identify if there are any methods or approaches that enables Scania to implement a functional hazard analyzes early in the development process of electrical systems and to analyze these.The results of this thesis shows that it is possible to start the FMEA process early in the development process of the electrical system if the engineers have a functional perspec-tive in mind when performing the risk analysis where they list and rank the functions that is provided by the electrical system and their failure modes, failure effects, failure de-tection, severity, probability and occurrence.By using a function based FMEA, the engineer(s) can identify and promptly handle the safety critical functions early in the development process of a electrical system.A existing functionality at Scania has been broken down into functions and a functional hazard analysis has been performed on these as a demonstration of how a function based FMEA can be carried out and look like

Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic

A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing, and the cost is a cumulative discounted functional of the system's state. We examine two versions of the problem: ``nonpreemptive,'' where service is uninterruptible, and ``preemptive,'' where service to a customer can be interrupted and then resumed, possibly at a different station. We study the problem in the asymptotic heavy traffic regime proposed by Halfin and Whitt, in which the arrival rates and the number of servers at each station grow without bound. The two versions of the problem are not, in general, asymptotically equivalent in this regime, with the preemptive version showing an asymptotic behavior that is, in a sense, much simpler. Under appropriate assumptions on the structure of the system we show: (i) The value function for the preemptive problem converges to $V$, the value of a related diffusion control problem. (ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value $V$. The construction of these policies is based on a Hamilton--Jacobi--Bellman equation associated with $V$.Comment: Published at http://dx.doi.org/10.1214/105051605000000601 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org