The expected number of critical percolation clusters intersecting a line segment

We study critical percolation on a regular planar lattice. Let $E_G(n)$ be the expected number of open clusters intersecting or hitting the line segment $[0,n]$. (For the subscript $G$ we either take $\mathbb{H}$, when we restrict to the upper halfplane, or $\mathbb{C}$, when we consider the full lattice). Cardy (2001) (see also Yu, Saleur and Haas (2008)) derived heuristically that $E_{\mathbb{H}}(n) = An + \frac{\sqrt{3}}{4\pi}\log(n) + o(\log(n))$, where $A$ is some constant. Recently Kov\'{a}cs, Igl\'{o}i and Cardy (2012) derived heuristically (as a special case of a more general formula) that a similar result holds for $E_{\mathbb{C}}(n)$ with the constant $\frac{\sqrt{3}}{4\pi}$ replaced by $\frac{5\sqrt{3}}{32\pi}$. In this paper we give, for site percolation on the triangular lattice, a rigorous proof for the formula of $E_{\mathbb{H}}(n)$ above, and a rigorous upper bound for the prefactor of the logarithm in the formula of $E_{\mathbb{C}}(n)$.Comment: Final version, appeared in Elect.Comm.Probab. 21 (2016

On the size of the largest cluster in 2D critical percolation

We consider (near-)critical percolation on the square lattice. Let M_n be the size of the largest open cluster contained in the box [-n,n]^2, and let pi(n) be the probability that there is an open path from O to the boundary of the box. It is well-known that for all 0< a < b the probability that M_n is smaller than an^2 pi(n) and the probability that M_n is larger than bn^2 pi(n) are bounded away from 0 as n tends to infinity. It is a natural question, which arises for instance in the study of so-called frozen-percolation processes, if a similar result holds for the probability that M_n is between an^2 pi(n) and bn^2 pi(n). By a suitable partition of the box, and a careful construction involving the building blocks, we show that the answer to this question is affirmative. The `sublinearity' of 1/pi(n) appears to be essential for the argument.Comment: 12 pages, 3 figures, minor change

The gaps between the sizes of large clusters in 2D critical percolation

Consider critical bond percolation on a large 2n by 2n box on the square lattice. It is well-known that the size (i.e. number of vertices) of the largest open cluster is, with high probability, of order n^2 \pi(n), where \pi(n) denotes the probability that there is an open path from the center to the boundary of the box. The same result holds for the second-largest cluster, the third largest cluster etcetera. Jarai showed that the differences between the sizes of these clusters is, with high probability, at least of order \sqrt{n^2 \pi(n)}. Although this bound was enough for his applications (to incipient infinite clusters), he believed, but had no proof, that the differences are in fact of the same order as the cluster sizes themselves, i.e. n^2 \pi(n). Our main result is a proof that this is indeed the case.Comment: 10 page

Breaks in the 45S rDNA Lead to Recombination-Mediated Loss of Repeats

rDNA repeats constitute the most heavily transcribed region in the human genome. Tumors frequently display elevated levels of recombination in rDNA, indicating that the repeats are a liability to the genomic integrity of a cell. However, little is known about how cells deal with DNA double-stranded breaks in rDNA. Using selective endonucleases, we show that human cells are highly sensitive to breaks in 45S but not the 5S rDNA repeats. We find that homologous recombination inhibits repair of breaks in 45S rDNA, and this results in repeat loss. We identify the structural maintenance of chromosomes protein 5 (SMC5) as contributing to recombination-mediated repair of rDNA breaks. Together, our data demonstrate that SMC5-mediated recombination can lead to error-prone repair of 45S rDNA repeats, resulting in their loss and thereby reducing cellular viability

A key role for stimulus-specific updating of the sensory cortices in the learning of stimulus-reward associations

Successful adaptive behavior requires the learning of associations between stimulus-specific choices and rewarding outcomes. Most research on the mechanisms underlying such processes has focused on subcortical reward-processing regions, in conjunction with frontal circuits. Given the extensive stimulus-specific coding in the sensory cortices, we hypothesized they would play a key role in the learning of stimulus-specific reward associations. We recorded electrical brain activity (EEG) during a learning-based, decision-making, gambling task where, on each trial, participants chose between a face and a house and then received feedback (gain or loss). Within each 20-trial set, either faces or houses were more likely to predict a gain. Results showed that early feedback processing (~200-1200ms) was independent of the choice made. In contrast, later feedback processing (~1400-1800ms) was stimulus-specific, reflected by decreased alpha power (reflecting increased cortical activity) over face-selective regions. For winning-versus-losing after a face choice, but not after a house choice. Finally, as the reward association was learned in a set, there was increasingly stronger attentional bias towards the more likely winning stimulus, reflected by increasing attentional-orienting-related brain activity and increasing likelihood of choosing that stimulus. These results delineate the processes underlying the updating of stimulus-reward associations during feedback-guided learning, which then guides future attentional allocation and decision making

Impaired Structural Motor Connectome in Amyotrophic Lateral Sclerosis

Amyotrophic lateral sclerosis (ALS) is a severe neurodegenerative disease selectively affecting upper and lower motor neurons. Patients with ALS suffer from progressive paralysis and eventually die on average after three years. The underlying neurobiology of upper motor neuron degeneration and its effects on the complex network of the brain are, however, largely unknown. Here, we examined the effects of ALS on the structural brain network topology in 35 patients with ALS and 19 healthy controls. Using diffusion tensor imaging (DTI), the brain network was reconstructed for each individual participant. The connectivity of this reconstructed brain network was compared between patients and controls using complexity theory without - a priori selected - regions of interest. Patients with ALS showed an impaired sub-network of regions with reduced white matter connectivity (p = 0.0108, permutation testing). This impaired sub-network was strongly centered around primary motor regions (bilateral precentral gyrus and right paracentral lobule), including secondary motor regions (bilateral caudal middle frontal gyrus and pallidum) as well as high-order hub regions (right posterior cingulate and precuneus). In addition, we found a significant reduction in overall efficiency (p = 0.0095) and clustering (p = 0.0415). From our findings, we conclude that upper motor neuron degeneration in ALS affects both primary motor connections as well as secondary motor connections, together composing an impaired sub-network. The degenerative process in ALS was found to be widespread, but interlinked and targeted to the motor connectome

Combined bead milling and enzymatic hydrolysis for efficient fractionation of lipids, proteins, and carbohydrates of Chlorella vulgaris microalgae

A combined bead milling and enzymatic hydrolysis process was developed for fractionation of the major valuable biomass components, i.e., proteins, carbohydrates, and lipids from the microalgae Chlorella vulgaris. The cells were treated by bead milling followed by hydrolysis with different hydrolytic enzymes, including lipase, phospholipase, protease, and cellulase. Without enzymatic hydrolysis, the recovery yield of lipids, carbohydrates, and proteins for bead milled biomass was 75%, 31%, and 40%, respectively, while by applying enzymatic treatments these results were improved significantly. The maximum recovery yield for all components was obtained after enzymatic hydrolysis of bead milled biomass by lipase at 37 degrees C and pH 7.4 for 24 h, yielding 88% lipids in the solid phase while 74% carbohydrate and 68% protein were separated in the liquid phase. The recovery yield of components after enzymatic hydrolysis of biomass without bead milling was 44% lower than that of the milled biomass.publishedVersionPaid Open Acces

Understanding mild cell disintegration of microalgae in bead mills for the release of biomolecules

Cell disintegration is, in general, the first step in the biorefinery of algae, since it allows the release of biomolecules of interest from the cells into the bulk medium. For high-value commercial applications, the disintegration process must be selective, energy efficient and mild. Developing a process with such features would demand extensive experimental effort. In the present study, we attempt to provide a tool for developing an efficient disintegration process via bead milling, by proposing a modelling strategy that allows the prediction of the kinetics of cell disintegration while having as input not only process parameters but also strain-specific parameters like cell size and cell-wall strength. The model was validated for two different algal strains (Tetraselmis suecica and Chlorella vulgaris), at various values of bead size (0.3–1 mm) and bead fillings (2.5–75%) and at two different scales of 80 and 500 mL. Since the kinetics of disintegration is proportional to the kinetics of release of biomolecules, the model can be further used for scale-up studies and to establish a window of operation to selectively target cells or metabolites of interest. Furthermore, the energy consumption in the mill was evaluated and it was found that operating at high bead fillings (>65%) is crucial to ensure an energy efficient process.publishedVersionPaid Open Acces

Selective fractionation of free glucose and starch from microalgae using aqueous two-phase systems

Microalgae are a promising source of lipids, pigments, proteins and carbohydrates, which are valuable compounds for many industries. However, optimal fractionation and valorization of all produced compounds is necessary to improve the economic viability of microalgae production. This paper aims to understand the fractionation of microalgae carbohydrates (free glucose and starch) in aqueous two-phase systems. Three aqueous two-phase systems were investigated to efficiently and mildly separate carbohydrates from disrupted Neochloris oleoabundans. This strain contains 16 w/w% of proteins, 48 w/w% total fatty acids and 27 w/w% carbohydrates when cultivated under saline water and nitrogen depletion conditions. The protein content decreases and the amount of fatty acids and carbohydrates increases notably under stress conditions and glucose becomes the main carbohydrate in this microalgae. Glucose is present in the disrupted microalgae as part of polymeric carbohydrates (starch) or in monomeric form (free glucose). With the aqueous two-phase system Polyethylene Glycol 400 - Cholinium dihydrogen phosphate (PEG400-ChDHp) microalgal free glucose is fractionated up to a recovery of 99% to the most hydrated bottom phase in a single step. Simultaneously, a recovery of 70% is reached for microalgal starch in the interface after two additional liquid-liquid extractions with PEG400-ChDHp. The final fractions obtained were free of pigments.publishedVersionPaid Open Acces