The WNT signaling pathway has an essential role in colorectal carcinogenesis and progression, which involves a cascade of genetic and epigenetic changes. We aimed to analyze DNA methylation affecting the WNT pathway genes in colorectal carcinogenesis in promoter and gene body regions using whole methylome analysis in 9 colorectal cancer, 15 adenoma, and 6 normal tumor adjacent tissue (NAT) samples by methyl capture sequencing. Functional methylation was confirmed on 5-aza-2′-deoxycytidine-treated colorectal cancer cell line datasets. In parallel with the DNA methylation analysis, mutations of WNT pathway genes (APC, β-catenin/CTNNB1) were analyzed by 454 sequencing on GS Junior platform. Most differentially methylated CpG sites were localized in gene body regions (95% of WNT pathway genes). In the promoter regions, 33 of the 160 analyzed WNT pathway genes were differentially methylated in colorectal cancer vs. normal, including hypermethylated AXIN2, CHP1, PRICKLE1, SFRP1, SFRP2, SOX17, and hypomethylated CACYBP, CTNNB1, MYC; 44 genes in adenoma vs. NAT; and 41 genes in colorectal cancer vs. adenoma comparisons. Hypermethylation of AXIN2, DKK1, VANGL1, and WNT5A gene promoters was higher, while those of SOX17, PRICKLE1, DAAM2, and MYC was lower in colon carcinoma compared to adenoma. Inverse correlation between expression and methylation was confirmed in 23 genes, including APC, CHP1, PRICKLE1, PSEN1, and SFRP1. Differential methylation affected both canonical and noncanonical WNT pathway genes in colorectal normal-adenoma-carcinoma sequence. Aberrant DNA methylation appears already in adenomas as an early event of colorectal carcinogenesis.

A simple theory of the detected current $I\left(t\right)$ flowing through charge qubits—quantum dots—is proposed in terms of standard continuous measurement theory. Applied to a double dot, our formalism easily confirms previous results on quantum Zeno effect, driven by growing ammeter performance $\gamma$. Due to the transparent formalism, we can calculate the exact fluctuation spectrum $S\left(\omega \right)$ of the detected current, containing a significant Lorentzian peak near the Rabi frequency of the double dot.

We analyze the difference between ex ante and ex post equilibria in classical games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we find a constructive procedure to find two-person Bayesian games with a nonlocal (i.e., no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle, and share the property that their relevant ex ante equilibria are ex post equilibria as well. We introduce here a different type of game, based on the Bell theorem by Vértesi and Bene, which does not have the latter property: The ex ante and ex post equilibria differ.

Understanding the structure of nonlocal correlations is important in many fields ranging from fundamental questions of physics to device-independent cryptography. We present a protocol that can convert extremal two-party–two-input nonlocal no-signaling boxes of any type into any other extremal two-party–two-input nonlocal no-signaling box perfectly. Our results are exact, and even though the number of required boxes cannot be determined in advance, their expected number is finite. Our protocol is adaptive and demonstrates for the first time the usefulness of using no-signaling boxes in different causal orders by the parties.

Quantum pseudo-telepathy games, such as the Mermin–Peres magic square and the doily game (DG), theoretically allow players to win with unit probability when using entangled quantum strategies. We quantitatively characterize the quantum advantage in these games and compare it with violations of two Bell inequalities: the Clauser–Horne–Shimony–Holt and the Collins–Gisin inequalities. The analysis is restricted to two families of two-qubit states: modified Werner states and Bell-diagonal states. For each case, we identify and quantify the regions of quantum state space that exhibit either a quantum advantage or a Bell inequality violation, relative to the set of all entangled states. Within these families, the DG encompasses a larger fraction of entangled states than the Mermin–Peres magic square game, although both cover significantly smaller regions of entangled states compared to those where Bell inequalities are violated. Although both approaches are fundamentally linked to quantum contextuality, our analysis of the examined two-qubit state families suggests that Bell inequalities are more effective at revealing entanglement, even if pseudo-telepathy games offer a more intuitive and conceptually appealing perspective.

We present a detailed analysis of the effect of quantum loss and decoherence in the Bell-CHSH scenario. Adopting a device-independent approach, we study the change in the bipartite conditional probability distribution, i.e., the behavior of the realized nonlocal box pair when the elements of the entangled qubit pair subjected to independent noisy quantum channels modeled by completely positive maps. As the verification of Bell inequalities is crucial in device-independent quantum cryptography, our considerations are instructive from the perspective of quantum realizations of nonlocal box pairs. We find that the impact of quantum channels cannot be described by an equivalent classical noise channel.