Kochen-Specker Sets and Generalized Orthoarguesian Equations

Every set (finite or infinite) of quantum vectors (states) satisfies generalized orthoarguesian equations ($n$OA). We consider two 3-dim Kochen-Specker (KS) sets of vectors and show how each of them should be represented by means of a Hasse diagram---a lattice, an algebra of subspaces of a Hilbert space--that contains rays and planes determined by the vectors so as to satisfy $n$OA. That also shows why they cannot be represented by a special kind of Hasse diagram called a Greechie diagram, as has been erroneously done in the literature. One of the KS sets (Peres') is an example of a lattice in which 6OA pass and 7OA fails, and that closes an open question of whether the 7oa class of lattices properly contains the 6oa class. This result is important because it provides additional evidence that our previously given proof of noa =< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form an infinite sequence of successively stronger equations.Comment: 16 pages and 5 figure

Monomer dynamics of a wormlike chain

We derive the stochastic equations of motion for a tracer that is tightly attached to a semiflexible polymer and confined or agitated by an externally controlled potential. The generalised Langevin equation, the power spectrum, and the mean-square displacement for the tracer dynamics are explicitly constructed from the microscopic equations of motion for a weakly bending wormlike chain by a systematic coarse-graining procedure. Our accurate analytical expressions should provide a convenient starting point for further theoretical developments and for the analysis of various single-molecule experiments and of protein shape fluctuations.Comment: 6 pages, 4 figure

Ultrafast sub-30 FS all-optical switching based on gallium phosphide

Gallium Phosphide (GaP) is one of the few available materials with strong optical nonlinearity and negligible losses in the visible ( >450 )and near-infrared regime. In this work, we demonstrate that a GaP film can generate sub-30 fs (full width at half maximum) transmission modulation of up to ⁓70% in the 600-1000 nm wavelength range. Nonlinear simulations using parameters measured by the Z-scan approach indicate that the transmission modulation arises from the optical Kerr effect and two-photon absorption. Due to the absence of linear absorption, no slower free-carrier contribution is detected. These findings place GaP as a promising ultrafast material for all-optical switching at modulation speeds of up to 20 THz

A Very High Speed True Random Number Generator with Entropy Assessment

International audienceThe proposed true random number generator (TRNG) exploits the jitter of events propagating in a self-timed ring (STR) to generate random bit sequences at a very high bit rate. It takes advantage of a special feature of STRs that allows the time elapsed between successive events to be set as short as needed, even in the order of picoseconds. If the time interval between the events is set in concordance with the clock jitter magnitude, a simple entropy extraction scheme can be applied to generate random numbers. The proposed STR-based TRNG (STRNG) follows AIS31 recommendations: by using the proposed stochastic model, designers can compute a lower entropy bound as a function of the STR characteristics (number of stages, oscillation period and jitter magnitude). Using the resulting entropy assessment, they can then set the compression rate in the arithmetic post-processing block to reach the required security level determined by the entropy per output bit. Implementation of the generator in two FPGA families confirmed its feasibility in digital technologies and also confirmed it can provide high quality random bit sequences that pass the statistical tests required by AIS31 at rates as high as 200 Mbit/s

The P-Loop Domain of Yeast Clp1 Mediates Interactions Between CF IA and CPF Factors in Pre-mRNA 3′ End Formation

Cleavage factor IA (CF IA), cleavage and polyadenylation factor (CPF), constitute major protein complexes required for pre-mRNA 3′ end formation in yeast. The Clp1 protein associates with Pcf11, Rna15 and Rna14 in CF IA but its functional role remained unclear. Clp1 carries an evolutionarily conserved P-loop motif that was previously shown to bind ATP. Interestingly, human and archaean Clp1 homologues, but not the yeast protein, carry 5′ RNA kinase activity. We show that depletion of Clp1 in yeast promoted defective 3′ end formation and RNA polymerase II termination; however, cells expressing Clp1 with mutant P-loops displayed only minor defects in gene expression. Similarly, purified and reconstituted mutant CF IA factors that interfered with ATP binding complemented CF IA depleted extracts in coupled in vitro transcription/3′ end processing reactions. We found that Clp1 was required to assemble recombinant CF IA and that certain P-loop mutants failed to interact with the CF IA subunit Pcf11. In contrast, mutations in Clp1 enhanced binding to the 3′ endonuclease Ysh1 that is a component of CPF. Our results support a structural role for the Clp1 P-loop motif. ATP binding by Clp1 likely contributes to CF IA formation and cross-factor interactions during the dynamic process of 3′ end formation

How much randomness can be extracted from memoryless Shannon entropy sources?

We revisit the classical problem: given a memoryless source having a certain amount of Shannon Entropy, how many random bits can be extracted? This question appears in works studying random number generators built from physical entropy sources. Some authors use a heuristic estimate obtained from the Asymptotic Equipartition Property, which yields roughly $n$ extractable bits, where $n$ is the total Shannon entropy amount. However the best known precise form gives only $n-O(\sqrt{\log(1/\epsilon) n})$, where $\epsilon$ is the distance of the extracted bits from uniform. In this paper we show a matching $n-\Omega(\sqrt{\log(1/\epsilon) n})$ upper bound. Therefore, the loss of $\Theta(\sqrt{\log(1/\epsilon) n})$ bits is necessary. As we show, this theoretical bound is of practical relevance. Namely, applying the imprecise AEP heuristic to a mobile phone accelerometer one might overestimate extractable entropy even by $100\%$, no matter what the extractor is. Thus, the ``AEP extracting heuristic\u27\u27 should not be used without taking the precise error into account

In silico Analysis of 3′-End-Processing Signals in Aspergillus oryzae Using Expressed Sequence Tags and Genomic Sequencing Data

To investigate 3′-end-processing signals in Aspergillus oryzae, we created a nucleotide sequence data set of the 3′-untranslated region (3′ UTR) plus 100 nucleotides (nt) sequence downstream of the poly(A) site using A. oryzae expressed sequence tags and genomic sequencing data. This data set comprised 1065 sequences derived from 1042 unique genes. The average 3′ UTR length in A. oryzae was 241 nt, which is greater than that in yeast but similar to that in plants. The 3′ UTR and 100 nt sequence downstream of the poly(A) site is notably U-rich, while the region located 15–30 nt upstream of the poly(A) site is markedly A-rich. The most frequently found hexanucleotide in this A-rich region is AAUGAA, although this sequence accounts for only 6% of all transcripts. These data suggested that A. oryzae has no highly conserved sequence element equivalent to AAUAAA, a mammalian polyadenylation signal. We identified that putative 3′-end-processing signals in A. oryzae, while less well conserved than those in mammals, comprised four sequence elements: the furthest upstream U-rich element, A-rich sequence, cleavage site, and downstream U-rich element flanking the cleavage site. Although these putative 3′-end-processing signals are similar to those in yeast and plants, some notable differences exist between them

The interaction of Pcf11 and Clp1 is needed for mRNA 3′-end formation and is modulated by amino acids in the ATP-binding site

Polyadenylation of eukaryotic mRNAs contributes to stability, transport and translation, and is catalyzed by a large complex of conserved proteins. The Pcf11 subunit of the yeast CF IA factor functions as a scaffold for the processing machinery during the termination and polyadenylation of transcripts. Its partner, Clp1, is needed for mRNA processing, but its precise molecular role has remained enigmatic. We show that Clp1 interacts with the Cleavage–Polyadenylation Factor (CPF) through its N-terminal and central domains, and thus provides cross-factor connections within the processing complex. Clp1 is known to bind ATP, consistent with the reported RNA kinase activity of human Clp1. However, substitution of conserved amino acids in the ATP-binding site did not affect cell growth, suggesting that the essential function of yeast Clp1 does not involve ATP hydrolysis. Surprisingly, non-viable mutations predicted to displace ATP did not affect ATP binding but disturbed the Clp1–Pcf11 interaction. In support of the importance of this interaction, a mutation in Pcf11 that disrupts the Clp1 contact caused defects in growth, 3′-end processing and transcription termination. These results define Clp1 as a bridge between CF IA and CPF and indicate that the Clp1–Pcf11 interaction is modulated by amino acids in the conserved ATP-binding site of Clp1

The Two-Component Sensor Kinase TcsC and Its Role in Stress Resistance of the Human-Pathogenic Mold Aspergillus fumigatus

Two-component signaling systems are widespread in bacteria, but also found in fungi. In this study, we have characterized TcsC, the only Group III two-component sensor kinase of Aspergillus fumigatus. TcsC is required for growth under hyperosmotic stress, but dispensable for normal growth, sporulation and conidial viability. A characteristic feature of the ΔtcsC mutant is its resistance to certain fungicides, like fludioxonil. Both hyperosmotic stress and treatment with fludioxonil result in a TcsC-dependent phosphorylation of SakA, the final MAP kinase in the high osmolarity glycerol (HOG) pathway, confirming a role for TcsC in this signaling pathway. In wild type cells fludioxonil induces a TcsC-dependent swelling and a complete, but reversible block of growth and cytokinesis. Several types of stress, such as hypoxia, exposure to farnesol or elevated concentrations of certain divalent cations, trigger a differentiation in A. fumigatus toward a “fluffy” growth phenotype resulting in white, dome-shaped colonies. The ΔtcsC mutant is clearly more susceptible to these morphogenetic changes suggesting that TcsC normally antagonizes this process. Although TcsC plays a role in the adaptation of A. fumigatus to hypoxia, it seems to be dispensable for virulence