Abstract:
In recent projects on operating-system verification, C and C++ data types are often formalized using a semantics that does not fully specify the precise byte encoding of objects. It is well-known that such an underspecified data-type semantics can be used to detect certain kinds of type errors. In general, however, underspecified data-type semantics are unsound: they assign well-defined meaning to programs that have undefined behavior according to the C and C++ language standards. A precise characterization of the type-correctness properties that can be enforced with underspecified data-type semantics is still missing. In this paper, we identify strengths and weaknesses of underspecified data-type semantics for ensuring type safety of low-level systems code. We prove sufficient conditions to detect certain classes of type errors and, finally, identify a trade-off between the complexity of underspecified data-type semantics and their type-checking capabilities.

Abstract:
By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary $sl_2$ embeddings we show that a large set $\cal W$ of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set $\cal W$ contains many known $W$ algebras such as $W_N$ and $W_3^{(2)}$. Our formalism yields a completely algorithmic method for calculating the W algebra generators and their operator product expansions, replacing the cumbersome construction of W algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that any $W$ algebra in $\cal W$ can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Therefore {\em any} realization of this semisimple affine Lie algebra leads to a realization of the $W$ algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolutions for all algebras in $\cal W$. Some examples are explicitly worked out.

Abstract:
In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.

Abstract:
In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the theory finite $W$-algebras, which is an important class of non-linear symmetries. In particular, we discuss both the classical and quantum theory and elaborate on several aspects of their representation theory. Some new results are presented. These include finite $W$ coadjoint orbits, real forms and unitary representation of finite $W$-algebras and Poincare-Birkhoff-Witt theorems for finite $W$-algebras. Also we present some new finite $W$-algebras that are not related to $sl(2)$ embeddings. At the end of the paper we investigate how one could construct physical theories, for example gauge field theories, that are based on non-linear algebras.

Abstract:
We study popular local search and greedy algorithms for scheduling. The performance guarantee of these algorithms is well understood, but the worst-case lower bounds seem somewhat contrived and it is questionable if they arise in practical applications. To find out how robust these bounds are, we study the algorithms in the framework of smoothed analysis, in which instances are subject to some degree of random noise. While the lower bounds for all scheduling variants with restricted machines are rather robust, we find out that the bounds are fragile for unrestricted machines. In particular, we show that the smoothed performance guarantee of the jump and the lex-jump algorithm are (in contrast to the worst case) independent of the number of machines. They are Theta(phi) and Theta(log(phi)), respectively, where 1/phi is a parameter measuring the magnitude of the perturbation. The latter immediately implies that also the smoothed price of anarchy is Theta(log(phi)) for routing games on parallel links. Additionally we show that for unrestricted machines also the greedy list scheduling algorithm has an approximation guarantee of Theta(log(phi)).

Abstract:
Several policy options have been discussed to mitigate the current subprime mortgage crisis. This paper analyses an interest rate freeze on adjustable rate mortgages as one possible reaction. In particular, the implications on Residential Mortgage Backed Securities (RMBS) are studied. We examine shifts in the underlying portfolio’s discounted cash flow distributions as well as changes in the payment profile of RMBS-tranches. We show that the positive effects of a rate freeze, e.g. less foreclosures and a stabilizing housing market, can outweigh the negative effect of lower interest income such that investors might be better off.

Abstract:
Purpose: The incidence of hyperplastic thyroid nodular disease has been consistently rising over the last decades. In addition, unsuspected papillary thyroid carcinoma (PTC) can be found in up to 34% of patients operated for benign thyroid lesions. PTC tends to occur multi-focally and is commonly of polyclonal origin. We set out to test the hypothesis that in benign thyroid disease, a unique genetic signature can already be identified in the benign pathology, which is associated with a susceptibility of the thyroid tissue to neoplastic transformation in the context of additional growth promoting stimuli. Patients and Methods: We obtained a set of 23 samples from patients with multinodular goiter (MNG), 12 of whom also harbored an unsuspected PTC. We used global gene expression analysis to evaluate for dissimilarities in the gene expression patterns between these two groups. We also compared these patterns to the profiles of 3 normal thyroid and 7 PTC samples. Results: We were able to accurately distinguish between hyperplastic nodules of patients with multinodular goiter and those that were associated with a PTC. One of the strongest differentially expressed genes, CDC42, has been implicated to respond to environmental factors such as UVB radiation and might point to novel factors contributing to PTC genesis in the setting of pre-existing benign proliferative disease. Conclusion: While the comparison between histologically identical samples cannot distinguish the two groups of goiters, unsupervised or supervised approaches allowed us to identify a molecular signature associated with PTC susceptibility in multinodular goiter.

This paper introduces a new datapath architecture for reconfigurable processors. The proposed datapath is based on Network-on-Chip approach and facilitates tight coupling of all functional units. Reconfigurable functional elements can be dynamically allocated for application specific optimizations, enabling polymorphic computing. Using a modified network simulator, performance of several NoC topologies and parameters are investigated with standard benchmark programs, including fine grain and coarse grain computations. Simulation results highlight the flexibility and scalability of the proposed polymorphic NoC processor for a wide range of application domains.

The discovery of non-linear systems dynamics has impacted concepts of knowledge to ascribe to it dynamic properties. It has expanded a development that finds its roots more than hundred years ago. Then, certainty was sought in systems of scientific insight. Such absolute certainty was inevitably static as it would be irrevocable once acquired. Although principal limits to the obtainability of knowledge were defined by scientific and philosophical advances from the 1920s through the mid-twentieth century, the knowledge accessible within those boundaries was considered certain, allowing detailed description and prediction within the recognized limits. The trend shifted away from static theories of knowledge with the discovery of the laws of nature underlying non-linear dynamics. The gnoseology of complex systems has built on insights of non-periodic flow and emergent processes to explain the underpinnings of generation and destruction of information and to unify deterministic and indeterministic descriptions of the world. It has thus opened new opportunities for the discourse of doing research.

Abstract:
Two highly visible, but conflicting concepts of morality have found widespread acceptance in philosophy. Socrates identified goodness with wisdom, holding lack of knowledge responsible for all moral mistakes. David Hume contrasted prescriptive with descriptive judgments, leading him to the conclusion that the former, unlike the latter, are not rationally supportable. It has often been missed that the acceptance of both, Socrates’ teachings and Hume’s law, generates a conflict, as elements of these two concepts contradict each other. It would appear prima facie obvious that mankind has learned from history how to coexist and make societies more just. Hence, there must be an empirical component contained in morals. Today, we have data that are reflective of certain elements of social justice. Measurables like crime rate, range between high and low income brackets, unemployment et cetera can serve as quantitative indicators for individual components that contribute to social justice. Such evidence corroborates at least a restriction on Hume’s stance, if not an outright negation. Because there are rational and empirical elements underlying morality, thought models need to be calibrated against the real world for validation. The discussion, what constitutes progress and social justice, must consult history and research—not ideology—as sources of justification. Philosophy and the sciences must cross-fertilize each other.