Single nucleotide polymorphism (SNP) discriminations by nanopore sensing

Single Nucleotide Polymorphisms (SNPs) are a common type of nucleotide alterations across the genome. A rapid but accurate detection of individual or SNP panels can lead to the right and in-time treatments which possibly save lives. In one of our studies, nanopore is introduced to rapidly detect BRAF 1799 T-A mutation (V600E), with the help of an Ap-dA cross-link right at the mutation site. These sequence-specific crosslinks are formed upon strong covalent interactions between probe based abasic sites (Ap) and target based deoxy-adenosine (dA) residues. Duplexes stabilized by the crosslink complexes create indefinite blocking signatures when captured in the nanopore, creating a high contrast compared to the "spike-like" translocations events produced by the un-crosslinked and wildtype duplexes. Those consistent blocking events couldn't be resolved unless an inverted voltage is applied. In a 1:1 BRAF mutant-wildtype mixture, the nanopore can successfully discriminate between the two sequences in a quantitative manner. In summary, nanopore paired with sequence-specific crosslink can detect a specific type of SNP with a high contrast manner. In another study, nanopore sensing is modified to be capable of detections with multiple SNPs in a single detection mix. To achieve this, an RNA homopolymer barcode is integrated into the probe sequence so nanopore can read out a distinctive level signature when the target-probe duplex is de-hybridizing through the pore. Since different RNA homopolymers (e.g. Poly rA and Poly rC) can generate signature levels distinctive from each other and other DNA sequences, they can be applied to generate characteristic patterns that simultaneously highlight multiple SNPs in the mixture. In this study, we assigned two different RNA barcodes (Poly rA and Poly rC) to label KRAS G12D and Tp53 R172H SNPs (both T[right arrow]A mutations) in the solution. During nanopore readout, the KRAS G12D containing duplex generates a "downward" step pattern but Tp53 R172H always has an "upward" step pattern, the high contrast between those two patterns makes recognition easy enough with naked eyes, and further statistical analysis is unnecessary. Theoretically, at least four different barcodes can be implemented at the same time, furthermore, the length of the barcode can also affect the barcode pattern. Thus, in theory, a panel of more than 10 SNPs can be identified simultaneously.Includes bibliographical reference

Universal Trade-off Between Irreversibility and Relaxation Timescale

We establish a general lower bound for the entropy production rate based on the Kullback-Leibler divergence and the Logarithmic-Sobolev constant that characterizes the time-scale of relaxation. This bound can be considered as an enhanced second law of thermodynamics. As a crucial application, we find a universal trade-off relation between the dissipation rate and relaxation timescale in thermal relaxation. Importantly, we show that a thermodynamic upper bound on the relaxation time between two given states follows directly from the trade-off relation, serving as an inverse speed limit throughout the entire time region. Our findings unveil some hidden universal behaviors of thermal relaxation processes, which can also be extended to open quantum systems.Comment: 6 + 7 pages, 1 figures. All comments are welcom

Fair and Optimal Classification via Transports to Wasserstein-Barycenter

Fairness in automated decision-making systems has gained increasing attention as their applications expand to real-world high-stakes domains. To facilitate the design of fair ML systems, it is essential to understand the potential trade-offs between fairness and predictive power, and the construction of the optimal predictor under a given fairness constraint. In this paper, for general classification problems under the group fairness criterion of demographic parity (DP), we precisely characterize the trade-off between DP and classification accuracy, referred to as the minimum cost of fairness. Our insight comes from the key observation that finding the optimal fair classifier is equivalent to solving a Wasserstein-barycenter problem under $\ell_1$-norm restricted to the vertices of the probability simplex. Inspired by our characterization, we provide a construction of an optimal fair classifier achieving this minimum cost via the composition of the Bayes regressor and optimal transports from its output distributions to the barycenter. Our construction naturally leads to an algorithm for post-processing any pre-trained predictor to satisfy DP fairness, complemented with finite sample guarantees. Experiments on real-world datasets verify and demonstrate the effectiveness of our approaches.Comment: Code is at https://github.com/rxian/fair-classificatio

CDO pricing using single factor MG-NIG copula model with stochastic correlation and random factor loading

AbstractWe consider the valuation of CDO tranches with single factor MG-NIG copula model, where the involved distributions are mixtures of Gaussian distribution and NIG distribution. In addition, we consider two cases for stochastic correlation and random factor loadings instead of constant factor loadings. We analyze the unconditional characteristic function of accumulated loss of the reference portfolio, and derive the loss distribution through the fast Fourier transform. Moreover, using the loss distribution and semi-analytic approach, we can get the CDO tranches spreads

Fast Functionalization with High Performance in the Autonomous Information Engine

Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register, or conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.Comment: 14 pages, 3 figures; all comments are welcom