Kazuki Nakamae, Takayuki Suzuki, Sora Yonezawa
et al.
Base-editing technologies, particularly cytosine base editors (CBEs), allow precise gene modification without introducing double-strand breaks; however, unintended RNA off-target effects remain a critical concern and are under studied. To address this gap, we developed the Pipeline for CRISPR-induced Transcriptome-wide Unintended RNA Editing (PiCTURE), a standardized computational pipeline for detecting and quantifying transcriptome-wide CBE-induced RNA off-target events. PiCTURE identifies both canonical ACW (W = A or T/U) motif-dependent and non-canonical RNA off-targets, revealing a broader WCW motif that underlies many unanticipated edits. Additionally, we developed two machine learning models based on the DNABERT-2 language model, termed STL and SNL, which outperformed motif-only approaches in terms of accuracy, precision, recall, and F1 score. To demonstrate the practical application of our predictive model for CBE-induced RNA off-target risk, we integrated PiCTURE outputs with the Predicting RNA Off-target compared with Tissue-specific Expression for Caring for Tissue and Organ (PROTECTiO) pipeline and estimated RNA off-target risk for each transcript showing tissue-specific expression. The analysis revealed differences among tissues: while the brain and ovaries exhibited relatively low off-target burden, the colon and lungs displayed relatively high risks. Our study provides a comprehensive framework for RNA off-target profiling, emphasizing the importance of advanced machine learning-based classifiers in CBE safety evaluations and offering valuable insights to inform the development of safer genome-editing therapies.
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension, and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-K\r{u}rka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension~1, but also dimension~1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension~ 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension.
We show that, in general, averaging at simple resonances a real-analytic, nearly-integrable Hamiltonian, one obtains a one-dimensional system with a cosine-like potential; ‘in general’ means for a generic class of holomorphic perturbations and apart from a finite number of simple resonances with small Fourier modes; ‘cosine-like’ means that the potential depends only on the resonant angle, with respect to which it is a Morse function with one maximum and one minimum. Furthermore, the (full) transformed Hamiltonian is the sum of an effective one-dimensional Hamiltonian (which is, in turn, the sum of the unperturbed Hamiltonian plus the cosine-like potential) and a perturbation, which is uniformly exponentially small. As a corollary, under the above hypotheses, if the unperturbed Hamiltonian is also strictly convex, the effective Hamiltonian at any simple resonance (apart a finite number of low-mode resonances) has the phase portrait of a pendulum. The results presented in this paper are an essential step in the proof (in the ‘mechanical’ case) of a conjecture by Arnold–Kozlov–Neishdadt [Arnold V I, Kozlov V V and Neishtadt A I 2006 Mathematical aspects of classical and celestial mechanics Encyclopaedia of Mathematical Sciences 3rd edn vol 3 (Berlin: Springer), remark 6.8, p 285], claiming that the measure of the ‘non-torus set’ in general nearly-integrable Hamiltonian systems has the same size of the perturbation; compare [Biasco L and Chierchia L 2015 On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems Rendiconti Lincei. Mat. Appl. 26 1–10 and Biasco L and Chierchia L KAM Theory for Secondary Tori (arXiv:1702.06480v1 [math.DS])].
There are two main reasons why relative equilibria of N point masses under the influence of Newton attraction are mathematically more interesting to study when space dimension is at least 4: On the one hand, in a higher dimensional space, a relative equilibrium is determined not only by the initial configuration but also by the choice of a complex structure on the space where the motion takes place; in particular, its angular momentum depends on this choice; On the other hand, relative equilibria are not necessarily periodic: if the configuration is "balanced" but not central, the motion is in general quasi-periodic. In this exploratory paper we address the following question, which touches both aspects: what are the possible frequencies of the angular momentum of a given central (or balanced) configuration and at what values of these frequencies bifurcations from periodic to quasi-periodic relative equilibria do occur ? We give a full answer for relative equilibrium motions in dimension 4 and conjecture that an analogous situation holds true for higher dimensions. A refinement of Horn's problem given by Fomin, Fulton, Li and Poon plays an important role. P.S. The conjecture is now proved (see Alain Chenciner and Hugo Jimenez Perez, Angular momentum and Horn's problem, arXiv:1110.5030v1 [math.DS]).
LFSR and NFSR are the basic building blocks in almost all the state of the art stream ciphers like Trivium and Grain-128. However, a number of attacks are mounted on these type of ciphers. Cellular Automata (CA) has recently been chosen as a suitable structure for crypto-primitives. In this work, a stream cipher is presented based on hybrid CA. The stream cipher takes 128 bit key and 128 bit initialization vector (IV) as input. It is designed to produce $\mathrm{2^{128}}$ random keystream bits and initialization phase is made faster 4 times than that of Grain-128. We also analyze the cryptographic strength of this cipher. Finally, the proposed cipher is shown to be resistant against known existing attacks.
Chris Kuhlman, Henning Mortveit, David Murrugarra
et al.
This paper characterizes the attractor structure of synchronous and asynchronous Boolean networks induced by bi-threshold functions. Bi-threshold functions are generalizations of standard threshold functions and have separate threshold values for the transitions $0 \rightarrow $1 (up-threshold) and $1 \rightarrow 0$ (down-threshold). We show that synchronous bi-threshold systems may, just like standard threshold systems, only have fixed points and 2-cycles as attractors. Asynchronous bi-threshold systems (fixed permutation update sequence), on the other hand, undergo a bifurcation. When the difference $\Delta$ of the down- and up-threshold is less than 2 they only have fixed points as limit sets. However, for $\Delta \geq 2$ they may have long periodic orbits. The limiting case of $\Delta = 2$ is identified using a potential function argument. Finally, we present a series of results on the dynamics of bi-threshold systems for families of graphs.
Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.
We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton.
This work considers a cellular automaton (CA) with two particles: a stationary particle $1$ and left-going one $\overline{1}$. When a $\overline{1}$ encounters a $1$, both particles annihilate. We derive asymptotic distribution of appearence of particles at a given site when the CA is initialized with the Bernoulli measure with the probabilities of both particles equal to $1/2$.
We give a functional limit law for the normalized profile of random plane-oriented recursive trees. The proof uses martingale convergence theorems in discrete and continuous-time. This complements results of Hwang (2007).
We discuss scaling limits of random planar maps chosen uniformly over the set of all $2p$-angulations with $n$ faces. This leads to a limiting space called the Brownian map, which is viewed as a random compact metric space. Although we are not able to prove the uniqueness of the distribution of the Brownian map, many of its properties can be investigated in detail. In particular, we obtain a complete description of the geodesics starting from the distinguished point called the root. We give applications to various properties of large random planar maps.
Michael Drmota, Bernhard Gittenberger, Alois Panholzer
We develop a combinatorial structure to serve as model of random real world networks. Starting with plane oriented recursive trees we substitute the nodes by more complex graphs. In such a way we obtain graphs having a global tree-like structure while locally looking clustered. This fits with observations obtained from real-world networks. In particular we show that the resulting graphs are scale-free, that is, the degree distribution has an asymptotic power law.
If the interest of stochastic L-systems for plant growth simulation and visualization is broadly acknowledged, their full mathematical potential has not been taken advantage of. In this article, we show how to link stochastic L-systems to multitype branching processes, in order to characterize the probability distributions and moments of the numbers of organs in plant structure. Plant architectural development can be seen as the combination of two subprocesses driving the bud population dynamics, branching and differentiation. By writing the stochastic L-system associated to each subprocess, we get the generating function associated to the whole system by compounding the associated generating functions. The modelling of stochastic branching is classical, but to model differentiation, we introduce a new framework based on multivariate phase-type random vectors.
We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We illustrate our results with applications to some known chains from computer science and statistical mechanics.
Gantert and Müller (2006) proved that a critical branching random walk (BRW) on the integer lattice is transient by analyzing this problem within the more general framework of branching Markov chains and making use of Lyapunov functions. The main purpose of this note is to show how the same result can be derived quite elegantly and even extended to the nonlattice case within the theory of weighted branching processes. This is done by an analysis of certain associated random weighted location measures which, upon taking expectations, provide a useful connection to the well established theory of ordinary random walks with i.i.d. increments. A brief discussion of the asymptotic behavior of the left- and rightmost particles in a critical BRW as time goes to infinity is provided in the final section by drawing on recent work by Hu and Shi (2008).
Severini and Mansour introduced $\textit{square polygons}$, as graphical representations of $\textit{square permutations}$, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.
Let $Z_n,n=0,1,\ldots,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $f_0(s),f_1(s),\ldots,$ and let $S_0=0$, $S_k=X_1+ \ldots +X_k,k \geq 1$, be the associated random walk with $X_i=\log f_{i-1}^{\prime}(1), \tau (m,n)$ be the left-most point of minimum of $\{S_k,k \geq 0 \}$ on the interval $[m,n]$, and $T=\min \{ k:Z_k=0\}$. Assuming that the associated random walk satisfies the Doney condition $P(S_n > 0) \to \rho \in (0,1), n \to \infty$, we prove (under the quenched approach) conditional limit theorems, as $n \to \infty$, for the distribution of $Z_{nt}, Z_{\tau (0,nt)}$, and $Z_{\tau (nt,n)}, t \in (0,1)$, given $T=n$. It is shown that the form of the limit distributions essentially depends on the location of $\tau (0,n)$ with respect to the point $nt$.
We study the number of records in random split trees on $n$ randomly labelled vertices. Equivalently the number of random cuttings required to eliminate an arbitrary random split tree can be studied. After normalization the distributions are shown to be asymptotically $1$-stable. This work is a generalization of our earlier results for the random binary search tree which is one specific case of split trees. Other important examples of split trees include $m$-ary search trees, quadtrees, median of $(2k+1)$-trees, simplex trees, tries and digital search trees.