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Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-order discrepancies between probability measures
No full textThis is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and engineering. The central object of our study is a new discrepancy d between two probability distributions in position and velocity states, which is reminiscent of the 2-Wasserstein distance, but of second-order nature. We construct d in two steps. First, we optimise over transport plans. The cost function is given by the minimal acceleration between two coupled states on a fixed time horizon T. Second, we further optimise over the time horizon T > 0. We prove the existence of optimal transport plans and maps, and study two time-continuous characterisations of d. One is given in terms of dynamical transport plans. The other one -- in the spirit of the Benamou--Brenier formula -- is formulated as the minimisation of an action of the acceleration field, constrained by Vlasov's equations. Equivalence of static and dynamical formulations of d holds true. While part of this result can be derived from recent, parallel developments in optimal control between measures, we give an original proof relying on two new ingredients: Galilean regularisation of Vlasov's equations and a kinetic Monge--Mather shortening principle. Finally, we establish a first-order differential calculus in the geometry induced by d, and identify solutions to Vlasov's equations with curves of measures satisfying a certain d-absolute continuity condition. One consequence is an explicit formula for the d-derivative of such curves
Improving prediction accuracy in chimeric proteins with windowed multiple sequence alignment
No full textA key step in protein structure prediction involves the detection of co-evolving pairs of residues, a signal for spatial proximity. This information is gleaned from multiple sequence alignment and underscores Alphafold’s structure prediction for almost every known protein. A simple means to create proteins beyond those found in nature, is by unnaturally fusing together two known proteins or protein parts. Here we demonstrate that structured peptides are predicted with significantly reduced accuracy when added to the terminal ends of scaffold proteins. Appending the multiple sequence alignment for the individual peptide tags to that of the scaffold protein often restores prediction accuracy. This work suggests that this windowed multiple sequence alignment approach can be a useful tool for predicting the structure of fused, chimeric proteins
The journey matters: Average parameter count over pre-training unifies sparse and dense scaling laws
No full textPruning eliminates unnecessary parameters in neural networks; it offers a promising solution to the growing computational demands of large language models (LLMs). While many focus on post-training pruning, sparse pre-training--which combines pruning and pre-training into a single phase--provides a simpler alternative. In this work, we present the first systematic exploration of optimal sparse pre-training configurations for LLMs through an examination of 80 unique pruning schedules across different sparsity levels and training durations. We find that initiating pruning at 25% of total training compute and concluding at 75% achieves near-optimal final evaluation loss. These findings provide valuable insights for efficient and effective sparse pre-training of LLMs. Furthermore, we propose a new scaling law that modifies the Chinchilla scaling law to use the average parameter count over pre-training. Through empirical and theoretical validation, we demonstrate that this modified scaling law accurately models evaluation loss for both sparsely and densely pre-trained LLMs, unifying scaling laws across pre-training paradigms. Our findings indicate that while sparse pre-training achieves the same final model quality as dense pre-training for equivalent compute budgets, it provides substantial benefits through reduced model size, enabling significant potential computational savings during inference
Insect sex chromosome evolution: Conservation, turnover, and mechanisms of dosage compensation
No full textSex chromosomes have evolved many times throughout the tree of life, and understanding what has shaped their unusual morphological, sequence, and regulatory features has been a long-standing goal. Most early insights into insect sex chromosome biology came from a few model species, such as the fruit fly Drosophila melanogaster, which limited broad-scale evolutionary inferences. More recently, extensive comparative genomics studies have uncovered several unexpected patterns, which we highlight in this review. First, we describe the conservation of the ancestral X chromosome over 450 million years but also its recurrent turnover (i.e. its reversal to an autosome when a new X chromosome arose) in at least one order. We then summarize classical and more recent findings on how insects modulate the expression of X-linked genes following the degradation of the Y chromosome and how the diverse mechanisms of dosage compensation identified may elucidate important principles of sex chromosome regulatory evolution
LIPIcs
No full textWe define and study classes of ω-regular automata for which the nondeterminism can be resolved by a policy that uses a combination of memory and randomness on any input word, based solely on the prefix read so far. We examine two settings for providing the input word to an automaton. In the first setting, called adversarial resolvability, the input word is constructed letter-by-letter by an adversary, dependent on the resolver’s previous decisions. In the second setting, called stochastic resolvability, the adversary pre-commits to an infinite word and reveals it letter-by-letter. In each setting, we require the existence of an almost-sure resolver, i.e., a policy that ensures that as long as the adversary provides a word in the language of the underlying nondeterministic automaton, the run constructed by the policy is accepting with probability 1.
The class of automata that are adversarially resolvable is the well-studied class of history-deterministic automata. The case of stochastically resolvable automata, on the other hand, defines a novel class. Restricting the class of resolvers in both settings to stochastic policies without memory introduces two additional new classes of automata. We show that the new automata classes offer interesting trade-offs between succinctness, expressivity, and computational complexity, providing a fine gradation between deterministic automata and nondeterministic automata
PMLR
No full textDeterministic Markov Decision Processes (DMDPs) are a mathematical framework for decision-making where the outcomes and future possible actions are deterministically determined by the current action taken. DMDPs can be viewed as a finite directed weighted graph, where in each step, the controller chooses an outgoing edge. An objective is a measurable function on runs (or infinite trajectories) of the DMDP, and the value for an objective is the maximal cumulative reward (or weight) that the controller can guarantee. We consider the classical mean-payoff (aka limit-average) objective, which is a basic and fundamental objective.
Howard's policy iteration algorithm is a popular method for solving DMDPs with mean-payoff objectives. Although Howard's algorithm performs well in practice, as experimental studies suggested, the best known upper bound is exponential and the current known lower bound is as follows: For the input size I, the algorithm requires (math formular) iterations, where (math formular) hides the poly-logarithmic factors, i.e., the current lower bound on iterations is sub-linear with respect to the input size. Our main result is an improved lower bound for this fundamental algorithm where we show that for the input size I, the algorithm requires (math formular) iterations
Too fast for spin flipping: Absence of chirality-induced spin selectivity in coherent electron transport through single-molecule junctions
No full textChirality-induced spin selectivity (CISS), which refers to the ability of chiral molecules to preferentially select spins during electron transfer, has attracted great attention during the past two decades. However, the theoretical and experimental understanding of the CISS effect remains preliminary. In this study, we demonstrate that there is no distinguishable CISS effect in the case of coherent electron transport through single chiral molecular junctions for a set of four molecule studied here. Our conclusion is based on statistical evaluations of thousands of single-molecule junctions across four different molecules with different origins of chirality measured by the scanning tunneling microscope-based break-junction technique. The experimental results for all molecules show no dependence on external magnetic field or chirality in both conductance and current–voltage measurements. In addition, ab initio Hartree-Fork calculations combined with the nonequilibrium Green’s function method reveal that the spin–orbit coupling within chiral junctions bound to a few gold atoms is generally too weak to induce detectable spin polarizations from spin flipping or spin filtering during the ultrafast electron-transport time scale. The absence of an observable CISS effect in the coherent electron-transport regime suggests that the effect may only be found in other electron-transfer regimes and requires further experimental and theoretical efforts to achieve a comprehensive understanding
Thermal transport of amorphous hafnia across the glass transition
No full textHeat transport in glasses over a wide temperature range is critical for applications in gate dielectrics and thermal insulators but remains poorly understood due to the challenges in modeling vibrational anharmonicity and configurational dynamics across the glass transition. Recent predictions show an unusual decrease in thermal conductivity (κ) with temperature in amorphous hafnia (a-HfO2), contrasting with the typical trend in glasses. Using molecular dynamics with a machine-learning-based neuroevolution potential, we compute κ of a-HfO2 from 50 K to 2000 K. At low temperatures, the Wigner transport equation captures both anharmonicity and quantum statistics. Above 1200 K, atomic diffusion invalidates the quasiparticle picture, and we resort to the Green–Kubo method to capture convective transport. We further extend the Wigner transport equation to supercooled a-HfO2, revealing the crucial role of low-frequency modes in facilitating heat transport. The computed κ, based on both Green–Kubo and Wigner transport theories, increases continuously with temperature up to 2000 K
The JWST Emission Line Survey (JELS): An untargeted search for H α emission line galaxies at z > 6 and their physical properties
No full textWe present the first results of the JWST Emission Line Survey (JELS). Utilizing the first NIRCam narrow-band imaging at 4.7 μm, over 63 arcmin2 in the PRIMER/COSMOS field, we have identified 609 emission line galaxy candidates. From these, we robustly selected 35 H α star-forming galaxies at z ∼ 6.1, with H α star-formation rates (SFRH α) of ∼ 0.9 − 15 M yr−1.
Combining our unique H α sample with the exquisite panchromatic data in the field, we explored their physical properties and star-formation histories, and compared these to a broad-band selected sample at z ∼ 6 which has offered vital new insights into the nature of high-redshift galaxies. UV-continuum slopes (β) were considerably redder for our H α sample (β ∼ −1.92)
compared to the broad-band sample (β ∼ −2.35). This was not due to dust attenuation as our H α sample was relatively dustpoor (median AV = 0.23); instead, we argue that the reddened slopes could be due to nebular continuum. We compared SFRH α and the UV-continuum-derived SFRUV to SED-fitted measurements averaged over canonical time-scales of 10 and 100 Myr (SFR10 and SFR100). We found an increase in recent SFR for our sample of H α emitters, particularly at lower stellar masses (< 109 M). We also found that SFRH α strongly traces SFR averaged over 10 Myr time-scales, whereas the UV-continuum overpredicts SFR on 100 Myr time-scales at low stellar masses. These results point to our H α sample undergoing ‘bursty’ star
formation. Our F356W z ∼ 6 sample showed a larger scatter in SFR10/SFR100 across all stellar masses, which has highlighted how narrow-band photometric selections of H α emitters are key to quantifying the burstiness of star-formation activity
Contractive coupling rates and curvature lower bounds for Markov chains
No full textContractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry–Émery sense) and geodesic convexity of some entropic functionals. In addition, we recall and give straightforward generalizations of some notions of coarse Ricci curvature, and we discuss some of their properties and relations with the concepts of couplings and coupling rates: as an application, we show exponential contraction of the p-Wasserstein distance for the heat flow in the aforementioned examples