Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser

On March 2004, Anshel, Anshel, Goldfeld, and Lemieux introduced the \emph{Algebraic Eraser} scheme for key agreement over an insecure channel, using a novel hybrid of infinite and finite noncommutative groups. They also introduced the \emph{Colored Burau Key Agreement Protocol (CBKAP)}, a concrete realization of this scheme. We present general, efficient heuristic algorithms, which extract the shared key out of the public information provided by CBKAP. These algorithms are, according to heuristic reasoning and according to massive experiments, successful for all sizes of the security parameters, assuming that the keys are chosen with standard distributions. Our methods come from probabilistic group theory (permutation group actions and expander graphs). In particular, we provide a simple algorithm for finding short expressions of permutations in $S_n$, as products of given random permutations. Heuristically, our algorithm gives expressions of length $O(n^2\log n)$, in time and space $O(n^3)$. Moreover, this is provable from \emph{the Minimal Cycle Conjecture}, a simply stated hypothesis concerning the uniform distribution on $S_n$. Experiments show that the constants in these estimations are small. This is the first practical algorithm for this problem for $n\ge 256$. Remark: \emph{Algebraic Eraser} is a trademark of SecureRF. The variant of CBKAP actually implemented by SecureRF uses proprietary distributions, and thus our results do not imply its vulnerability. See also arXiv:abs/12020598Comment: Final version, accepted to Advances in Applied Mathematics. Title slightly change

Interoception and psychopathology: A developmental neuroscience perspective

Interoception refers to the perception of the physiological condition of the body, including hunger, temperature, and heart rate. There is a growing appreciation that interoception is integral to higher-order cognition. Indeed, existing research indicates an association between low interoceptive sensitivity and alexithymia (a difficulty identifying one’s own emotion), underscoring the link between bodily and emotional awareness. Despite this appreciation, the developmental trajectory of interoception across the lifespan remains under-researched, with clear gaps in our understanding. This qualitative review and opinion paper provides a brief overview of interoception, discussing its relevance for developmental psychopathology, and highlighting measurement issues, before surveying the available work on interoception across four stages of development: infancy, childhood, adolescence and late adulthood. Where gaps in the literature addressing the development of interoception exist, we draw upon the association between alexithymia and interoception, using alexithymia as a possible marker of atypical interoception. Evidence indicates that interoceptive ability varies across development, and that this variance correlates with established age-related changes in cognition and with risk periods for the development of psychopathology. We suggest a theory within which atypical interoception underlies the onset of psychopathology and risky behaviour in adolescence, and the decreased socio-emotional competence observed in late adulthood

Testing of the topoisomerase 1 inhibitor Genz-644282 by the pediatric preclinical testing program

Background Genz-644282 is a novel non-camptothecin topoisomerase I poison that is in clinical development. Procedures. Genz-644282 was tested against the PPTP in vitro panel (0.1 nM to 1 mu M), and in vivo using three times per week x 2 schedule repeated at day 21 at its maximum tolerated dose (MTD) of 4 mg/kg. Subsequently Genz-644282 was tested at 4, 3, 2, and 1 mg/kg in 3 models to assess the dose-response relationship. mRNA gene signatures predictive for Genz-644282 response in vitro were applied to select 15 tumor models that were evaluated prospectively. Results. In vitro, Genz-644282 demonstrated potent cytotoxic activity with a median IC(50) of 1.2 nM (range 0.2-21.9 nM). In vivo, Genz-644282 at its MTD (4 mg/kg) induced maintained complete responses (MCR) in 6/6 evaluable solid tumor models. At 2 mg/kg Genz-644282 induced CR or MCR in 3/3 tumor models relatively insensitive to topotecan, but there were no objective responses at 1 mg/kg. Further testing at 2 mg/kg showed that Genz-644282 induced objective regressions in 7 of 17 (41%) models. There was a significant correlation between predictive response scores based on Affymetrix U133Plus2 baseline tumor expression profiles and the observed in vivo responses to Genz-644282. Conclusions. Genz-644282 was highly active within a narrow dose range (2-4 mg/kg), typical of other topoisomerase I poisons. As with other topoisomerase I poisons, how accurately these data will translate to clinical activity will depend upon the drug exposures that can be achieved in children treated with this agent