Analogies between linguistics and information theory

An analogy is established between the syntagm and paradigm from Saussurean linguistics and the message and messages for selection from the information theory initiated by Claude Shannon. The analogy is pursued both as an end itself and for its analytic value in understanding patterns of retrieval from full text systems. The multivalency of individual words when isolated from their syntagm is contrasted with the relative stability of meaning of multi-word sequences, when searching ordinary written discourse. The syntagm is understood as the linear sequence of oral and written language. Saussureâ??s understanding of the word, as a unit which compels recognition by the mind, is endorsed, although not regarded as final. The lesser multivalency of multi-word sequences is understood as the greater determination of signification by the extended syntagm. The paradigm is primarily understood as the network of associations a word acquires when considered apart from the syntagm. The restriction of information theory to expression or signals, and its focus on the combinatorial aspects of the message, is sustained. The message in the model of communication in information theory can include sequences of written language. Shannonâ??s understanding of the written word, as a cohesive group of letters, with strong internal statistical influences, is added to the Saussurean conception. Sequences of more than one word are regarded as weakly correlated concatenations of cohesive units.

Molecular Computational Elements Encode Large Populations of Small Objects

Since the introduction of molecular computation1, 2, experimental molecular computational elements have grown3, 4, 5 to encompass small-scale integration6, arithmetic7 and games8, among others. However, the need for a practical application has been pressing. Here we present molecular computational identification (MCID), a demonstration that molecular logic and computation can be applied to a widely relevant issue. Examples of populations that need encoding in the microscopic world are cells in diagnostics or beads in combinatorial chemistry (tags). Taking advantage of the small size9 (about 1 nm) and large 'on/off' output ratios of molecular logic gates and using the great variety of logic types, input chemical combinations, switching thresholds and even gate arrays in addition to colours, we produce unique identifiers for members of populations of small polymer beads (about 100 m) used for synthesis of combinatorial libraries10, 11. Many millions of distinguishable tags become available. This method should be extensible to far smaller objects, with the only requirement being a 'wash and watch' protocol12. Our focus on converting molecular science into technology concerning analog sensors13, 14, turns to digital logic devices in the present work.

Scheduling and Platforming Trains at Busy Complex Stations

We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using ''manual'' methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network.Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Liquid source misted chemical deposition process of three-dimensional nano-ferroelectrics with substrate heating

A modification of liquid source misted chemical deposition process (LSMCD) with heating mist and substrate has developed, and this enabled to control mist penetrability and fluidity on sidewalls of three-dimensional structures and ensure step coverage. A modified LSMCD process allowed a combinatorial approach of Pb(Zr,Ti)O-3 (PZT) thin films and carbon nanotubes (CNTs) toward ultrahigh integration density of ferroelectric random access memories (FeRAMs). The CNTs templates were survived during the crystallization process of deposited PZT film onto CNTs annealed at 650 degrees C in oxygen ambient due to a matter of minute process, so that the thermal budget is quite small. The modified LSMCD process opens up the possibility to realize the nanoscale capacitor structure of ferroelectric PZT film with CNTs electrodes toward ultrahigh integration density FeRAMs.

K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.

Simple method for the rapid simultaneous screening of photocatalytic activity over multiple positions of self-cleaning films

An intelligent ink, previously shown to be capable of rapidly assessing photocatalytic activity, was simply applied via a felt-pen onto a commercially available piece of Activ (TM) self-cleaning glass. The ink, comprising of redox dye resazurin and the sacrificial electron donor glycerol within an aqueous hydroxy ethyl cellulose (HEC) polymer media, was photocatalytically degraded in a two-step process. The key initial stage was the photo-reductive conversion of resazurin to resorufin, whereby a colour change from blue to pink occurred. The latter stage was the subsequent photo-reduction of the resorufin, where a slower change from pink to colourless was seen. Red and green components of red-green-blue colour extracted from flat-bed scanner digital images of resazurin ink coated photocatalytic films at intervals during the photocatalysis reaction were inversely proportional to the changes seen via UV-visible absorption spectroscopy and indicative of reaction kinetics. A 3 x 3 grid of intelligent ink was drawn onto a piece of Activ (TM) and a glass blank. The photocatalysis reaction was monitored solely by flat-bed digital scanning. Red-green-blue values of respective positions on the grid were extracted using a custom-built program entitled RGB Extractor (c). The program was capable of extracting a number of 5 x 5 pixel averages of red-green-blue components simultaneously. Allocation of merely three coordinates allowed for the automatic generation of a grid, with scroll-bars controlling the number of positions to be extracted on the grid formed. No significant change in red and green components for any position on the glass blank was observed; however, the Activ (TM) film displayed a homogenous photo-reduction of the dye, reaching maxima in red and minima in green components in 23 +/- 3 and 14 +/- 2 min, respectively. A compositionally graded N-doped titania film synthesised in house via a combinatorial APCVD reaction was also photocatalytically tested by this method where 247 positions on a 13 x 19 grid were simultaneously analysed. The dramatic variation in photocatalysis observed was rapidly quantified for all positions (2-3 hours) allowing for correlations to be made between thicknesses and N : Ti% compositions attained from Swanepoel and WDX analysis, respectively. N incorporation within this system was found to be detrimental to film activity for the photocatalysis reaction of intelligent ink under 365 nm light.

TAZ Expression as a Prognostic Indicator in Colorectal Cancer

The Hippo pathway restricts the activity of transcriptional coactivators TAZ (WWTR1) and YAP. TAZ and YAP are reported to be overexpressed in various cancers, however, their prognostic significance in colorectal cancers remains unstudied. The expression levels of TAZ and YAP, and their downstream transcriptional targets, AXL and CTGF, were extracted from two independent colon cancer patient datasets available in the Gene Expression Omnibus database, totaling 522 patients. We found that mRNA expressions of both TAZ and YAP were positively correlated with those of AXL and CTGF (p<0.05). High level mRNA expression of TAZ, AXL or CTGF significantly correlated with shorter survival. Importantly, patients co-overexpressing all 3 genes had a significantly shorter survival time, and combinatorial expression of these 3 genes was an independent predictor for survival. The downstream target genes for TAZ-AXL-CTGF overexpression were identified by Java application MyStats. Interestingly, genes that are associated with colon cancer progression (ANTXR1, EFEMP2, SULF1, TAGLN, VCAN, ZEB1 and ZEB2) were upregulated in patients co-overexpressing TAZ-AXL-CTGF. This TAZ-AXL-CTGF gene expression signature (GES) was then applied to Connectivity Map to identify small molecules that could potentially be utilized to reverse this GES. Of the top 20 small molecules identified by connectivity map, amiloride (a potassium sparing diuretic,) and tretinoin (all-trans retinoic acid) have shown therapeutic promise in inhibition of colon cancer cell growth. Using MyStats, we found that low level expression of either ANO1 or SQLE were associated with a better prognosis in patients who co-overexpressed TAZ-AXL-CTGF, and that ANO1 was an independent predictor of survival together with TAZ-AXL-CTGF. Finally, we confirmed that TAZ regulates Axl, and plays an important role in clonogenicity and non-adherent growth in vitro and tumor formation in vivo. These data suggest that TAZ could be a therapeutic target for the treatment of colon cancer.

Zero-One Designs Produce Small Hard SAT Instances

Some basics of combinatorial block design are combined with certain constraint satisfaction problems of interest to the satisfiability community. The paper shows how such combinations lead to satisfiability problems, and shows empirically that these are some of the smallest very hard satisfiability problems ever constructed. Partially balanced (0,1) designs (PB01Ds) are introduced as an extension of balanced incomplete block designs (BIBDs) and (0,1) designs. Also, (0,1) difference sets are introduced as an extension of certain cyclical difference sets. Constructions based on (0,1) difference sets enable generation of PB01Ds over a much wider range of parameters than is possible for BIBDs. Building upon previous work of Spence, it is shown how PB01Ds lead to small, very hard, unsatisfiable formulas. A new three-dimensional form of combinatorial block design is introduced, and leads to small, very hard, satisfiable formulas. The methods are validated on solvers that performed well in the SAT 2009 and earlier competitions.

Nonlinear scattering by anisotropic dielectric periodic structures

The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures. © 2012 O. V. Shramkova and A. G. Schuchinsky.

Gaussian pulse mixing and scattering by finite nonlinear layered structures

Multiple Gaussian pulse interactions and scattering in the nonlinear layered dielectric structures have been examined. The Gaussian pulses with different centre frequencies and lengths are incident at oblique angles on the finite stack of nonlinear dielectric layers. The properties of the reflected and refracted waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed. It is shown that the efficiency of forward emission at the combinatorial frequency can be considerably increased when the wavelengths of interacting pulses are close to the edges of electromagnetic bandgap. © 2012 IEEE.

Three-wave Nonlinear Scattering by Quasiperiodic Dielectric Structure

The combinatorial frequency generation by a Fibonacci type quasi-periodic dielectric multilayered structure illuminated by two plane waves has been analysed. The effects of the layer parameters and Fibonacci sequence order on the properties of the combinatorial frequency waves emitted from the stacked nonlinear layers are discussed.