A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets

Face-to-face and edge-to-edge free energy interactions of Wyoming Na-montmorillonite platelets were studied by calculating potential of mean force along their center to center reaction coordinate using explicit solvent (i.e., water) molecular dynamics and free energy perturbation methods. Using a series of configurations, the Gay-Berne potential was parametrized and used to examine the meso-scale aggregation and properties of platelets that are initially random oriented under isothermal-isobaric conditions. Aggregates of clay were defined by geometrical analysis of face-to-face proximity of platelets with size distribution described by a log-normal function. The isotropy of the microstructure was assessed by computing a scalar order parameter. The number of platelets per aggregate and anisotropy of the microstructure both increases with platelet plan area. The system becomes more ordered and aggregate size increases with increasing pressure until maximum ordered state at confining pressure of 50 atm. Further increase of pressure slides platelets relative to each other leading to smaller aggregate size. The results show aggregate size of (3–8) platelets for sodium-smectite in agreement with experiments (3–10). The geometrical arrangement of aggregates affects mechanical properties of the system. The elastic properties of the meso-scale aggregate assembly are reported and compared with nanoindentation experiments. It is found that the elastic properties at this scale are close to the cubic systems. The elastic stiffness and anisotropy of the assembly increases with the size of the platelets and the level of external pressure.National Science Foundation (U.S.) (Extreme Science and Engineering Discovery Environment (XSEDE) and Texas Advanced Computing Center Grant TG-DMR100028)X-Shale Hub at MITSingapore-MIT Alliance for Research and Technolog

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter "d" going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a delta-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of "d" gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a delta-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of "d", for given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An improved and corrected examination of the long chain limit will appear as a separate posting. 32 pages, 9 postscript figures, LaTe

The microbial ferrous wheel in a neutral pH groundwater seep

Evidence for microbial Fe redox cycling was documented in a circumneutral pH ground-water seep near Bloomington, Indiana. Geochemical and microbiological analyses were conducted at two sites, a semi-consolidated microbial mat and a floating puffball structure. In situ voltammetric microelectrode measurements revealed steep opposing gradients of o2 and Fe(I I) at both sites, similar to other groundwater seep and sedimentary environments known to support microbial Fe redox cycling. The puffball structure showed an abrupt increase in dissolved Fed I) just at its surface (~5cm depth), suggesting an internal Fe(I I) source coupled to active Fed 1I) reduction. Most probable number enumerations detected microaerophilic Fe(II)-oxidizing bacteria (FeoB) and dissimilatory Fe(III)-reducing bacteria (FeRB) at densities of 102 to 105 cells ml_~1 in samples from both sites. In vitro Fed 1I) reduction experiments revealed the potential for immediate reduction (no lag period) of native Fe(III) oxides. Conventional full-length 16S rRNA gene clone libraries were compared with high throughput barcode sequencing of theV1, V4, orV6 variable regions of 16S rRNA genes in order to evaluate the extent to which new sequencing approaches could provide enhanced insight into the composition of Fe redox cycling microbial community structure. The composition of the clone libraries suggested a lithotroph-dominated microbial community centered around taxa related to known FeoB (e.g., Gallionella, Sideroxydans, Aquabacterium). Sequences related to recognized FeRB (e.g., Rhodoferax, Aeromonas, Geobacter, Desulfovibrio) were also well-represented. overall, sequences related to known FeoB and FeRB accounted for 88 and 59% of total clone sequences in the mat and puffball libraries, respectively. Taxa identified in the barcode libraries showed partial overlap with the clone libraries, but were not always consistent across different variable regions and sequencing platforms. However, the barcode libraries provided confirmation of key clone library results (e.g., the predominance of Betaproteobacteria) and an expanded view of lithotrophic microbial community composition

Diagenetic Crystal Growth in the Murray Formation, Gale Crater, Mars

The Pahrump region (Gale Crater, Mars) marks a critical transition between sedimentary environments dominated by alluvial-to-fluvial materials associated with the Gale crater rim, and depositional environments fundamentally linked to the crater's central mound, Mount Sharp. At Pahrump, the Murray formation consists of an approximately 14-meter thick succession dominated by massive to finely laminated mudstone with occasional interbeds of cross-bedded sandstone, and is best interpreted as a dominantly lacustrine environment containing tongues of prograding fluvial material. Murray formation mudstones contain abundant evidence for early diagenetic mineral precipitation and its subsequent removal by later diagenetic processes. Lenticular mineral growth is particularly common within lacustrine mudstone deposits at the Pahrump locality. High-resolution MAHLI images taken by the Curiosity rover permit detailed morphological and spatial analysis of these features. Millimeter-scale lenticular features occur in massive to well-laminated mudstone lithologies and are interpreted as pseudomorphs after calcium sulfate. The distribution and orientation of lenticular features suggests deposition at or near the sediment-water (or sediment-air) interface. Retention of chemical signals similar to host rock suggests that original precipitation was likely poikilotopic, incorporating substantial amounts of the primary matrix. Although poikilotopic crystal growth is common in burial environments, it also occurs during early diagenetic crystal growth within unlithified sediment where high rates of crystal growth are common. Loss of original calcium sulfate mineralogy suggests dissolution by mildly acidic, later-diagenetic fluids. As with lenticular voids observed at Meridiani by the Opportunity Rover, these features indicate that calcium sulfate deposition may have been widespread on early Mars; dissolution of depositional and early diagenetic minerals is a likely source for both calcium and sulfate ion-enrichment in burial fluids that precipitated in ubiquitous late-stage hydrofracture vein

Role of cellular senescence and NOX4-mediated oxidative stress in systemic sclerosis pathogenesis.

Systemic sclerosis (SSc) is a systemic autoimmune disease characterized by progressive fibrosis of skin and numerous internal organs and a severe fibroproliferative vasculopathy resulting frequently in severe disability and high mortality. Although the etiology of SSc is unknown and the detailed mechanisms responsible for the fibrotic process have not been fully elucidated, one important observation from a large US population study was the demonstration of a late onset of SSc with a peak incidence between 45 and 54 years of age in African-American females and between 65 and 74 years of age in white females. Although it is not appropriate to consider SSc as a disease of aging, the possibility that senescence changes in the cellular elements involved in its pathogenesis may play a role has not been thoroughly examined. The process of cellular senescence is extremely complex, and the mechanisms, molecular events, and signaling pathways involved have not been fully elucidated; however, there is strong evidence to support the concept that oxidative stress caused by the excessive generation of reactive oxygen species may be one important mechanism involved. On the other hand, numerous studies have implicated oxidative stress in SSc pathogenesis, thus, suggesting a plausible mechanism in which excessive oxidative stress induces cellular senescence and that the molecular events associated with this complex process play an important role in the fibrotic and fibroproliferative vasculopathy characteristic of SSc. Here, recent studies examining the role of cellular senescence and of oxidative stress in SSc pathogenesis will be reviewed

Age-related delay in information accrual for faces: Evidence from a parametric, single-trial EEG approach

Background: In this study, we quantified age-related changes in the time-course of face processing by means of an innovative single-trial ERP approach. Unlike analyses used in previous studies, our approach does not rely on peak measurements and can provide a more sensitive measure of processing delays. Young and old adults (mean ages 22 and 70 years) performed a non-speeded discrimination task between two faces. The phase spectrum of these faces was manipulated parametrically to create pictures that ranged between pure noise (0% phase information) and the undistorted signal (100% phase information), with five intermediate steps. Results: Behavioural 75% correct thresholds were on average lower, and maximum accuracy was higher, in younger than older observers. ERPs from each subject were entered into a single-trial general linear regression model to identify variations in neural activity statistically associated with changes in image structure. The earliest age-related ERP differences occurred in the time window of the N170. Older observers had a significantly stronger N170 in response to noise, but this age difference decreased with increasing phase information. Overall, manipulating image phase information had a greater effect on ERPs from younger observers, which was quantified using a hierarchical modelling approach. Importantly, visual activity was modulated by the same stimulus parameters in younger and older subjects. The fit of the model, indexed by R2, was computed at multiple post-stimulus time points. The time-course of the R2 function showed a significantly slower processing in older observers starting around 120 ms after stimulus onset. This age-related delay increased over time to reach a maximum around 190 ms, at which latency younger observers had around 50 ms time lead over older observers. Conclusion: Using a component-free ERP analysis that provides a precise timing of the visual system sensitivity to image structure, the current study demonstrates that older observers accumulate face information more slowly than younger subjects. Additionally, the N170 appears to be less face-sensitive in older observers