The replication dynamics (differential equation system) is the foundation of evolutionary game theory. When n=2, there are four possible types of replication dynamics. When n=3, there are 49 possible types of replication dynamics. However, when n>3, the classification of replication dynamics has not been solved. In this article, the sufficient and necessary conditions of the replication dynamics equation with a unique fixed point in the interior of simplex $S_n$(Int$S_n$) for $n\geq 2$ are presented. Furthermore, the different types of replication dynamics equations with a unique fixed point in IntSn is discussed.

We propose uncommon self-knowledge (USK) as a candidate criterion for consciousness: synergistic information a system carries about itself that exists only in the joint of its subsystems and is destroyed by decomposition. Drawing on Gottwald's partition-lattice grounding of Partial Information Decomposition (PID), where redundancy corresponds to Aumann's common knowledge and synergy to the gap between separate and joint observation, we propose the synergistic component of self-directed information as a candidate formal signature for conscious processing. If correct, the framework would (1) offer a clean separation between consciousness and metacognition (synergistic vs. redundant self-knowledge), (2) provide principled resolutions to counterexamples that challenge IIT, GWT, and HOT, (3) be operationalizable via Partial Information Rate Decomposition (PIRD) with self-targeting, and (4) generate distinctive empirical predictions, the strongest being a GWT timing dissociation (consciousness correlates with pre-broadcast synergy formation, not broadcast itself) and a specific dissociation between self-report disruption and task-performance disruption under middle-layer perturbation in LLMs. The proposal is consistent with recent empirical findings that both anaesthesia and Alzheimer's disease specifically reduce synergistic information processing while preserving or increasing redundancy.

Clinical interpretation often assumes that observable performance provides sufficient information about the organization of an adaptive system. However, similar observable performance may correspond to distinct latent organizations. This study extends a previous multi-level framework by introducing a fourth analytical level centered on longitudinal viability. Using an exploratory single-case design in a Parkinsonian patient, gait data were recorded with instrumented insoles under three occlusal conditions: neutral natural occlusion (ONL), a 2.5-degree increase in vertical dimension of occlusion (OC2.5), and a 3-degree increase in vertical dimension of occlusion (OC3). Two measurement sessions were conducted eleven weeks apart, during which the participant underwent a structured sensorimotor intervention. The vertical dimension of occlusion was considered as an experimentally varied constraint applied to an adaptive neuromechanical system. Although observable performance remained globally comparable across conditions, PCA-based latent-space analysis revealed differentiated longitudinal centroid displacements. OC3 exhibited the smallest displacement, ONL an intermediate displacement, and OC2.5 the largest displacement. This hierarchy supports the relevance of a Level 4 framework centered on viability, understood here as an exploratory proxy for a configuration's capacity to maintain lower longitudinal reorganization over time. These findings remain within-subject, exploratory, and non-causal. They do not establish a validated clinical threshold, causal occlusal effect, or therapeutic optimum. More generally, the work suggests that clinical relevance cannot be inferred solely from instantaneous performance or static latent structure, but may also depend on the capacity of a configuration to sustain a coherent trajectory over time.

In this work, we introduce a Tropical Axial Attention neural reasoning architecture that replaces vanilla softmax dot-product attention with max-plus operators, inducing a piecewise-linear structure aligned with dynamic programming formulations. From multi-species sequence alignments, our model learns all possible pairwise distances and is trained using a combination of $\ell_1$ and tropical symmetric distance metric losses with an ultrametric violation penalty. We leverage the well known isomorphic relationship between the space of all phylogenetic trees with $n$ species and tropical Grassmannian to show that tropical attention provides a natural geometric framework for phylogenetic inference. On empirical $DS1-DS11$ alignments, where true trees are unknown, the tropical model produces distance matrices that are substantially closer to their BME-induced tree metrics than the baseline models. These results suggest that tropical attention is a useful geometric inductive bias for neural phylogenetic inference, especially under distribution shift and when tree-metric consistency is important.

We propose a novel multimodal deep learning framework for patient-level survival prediction, which integrates whole-slide histology features, RNA-seq expression profiles, and clinical variables. Our architecture combines an ABMIL module~\cite{ilse2018attention} for slide-level representation with feedforward encoders for RNA and clinical data. These embeddings are then integrated through low-rank bilinear cross-modal fusion~\cite{liu2018efficient} to model conditional interactions across modalities while controlling parameter growth. The model outputs continuous risk scores that are subsequently mapped to survival times using a nonparametric calibration procedure based on the Kaplan--Meier estimator~\cite{kaplan1958nonparametric}. By decomposing multimodal reasoning into independent pairwise interactions, the proposed fusion design promotes structural interpretability and parameter efficiency compared with full tensor and hierarchical fusion strategies. Experiments on the CHIMERA challenge dataset demonstrate improved predictive performance over concatenation-based baselines and competitive generalization on hidden evaluation cohorts. These results indicate that the proposed framework is a promising approach for multimodal survival prediction in HR-NMIBC. The implementation is publicly available at this https URL.

Protein function prediction is dominated by representations grounded in sequence and static structure, neither of which captures the collective vibrational dynamics through which proteins act. Here we introduce frequency-space mechanics, a representational framework in which a protein is encoded as a mechanical harmonics graph (MHG): nodes are vibrational modes derived from molecular dynamics, and edges are harmonic couplings weighted by octave alignment between mode frequencies. The representation is coordinate-free, sequence-independent, scale-invariant, and inhabits a latent mechanical space in which the original atomic coordinates have been projected out. The same construction applies to any system with a tractable eigendecomposition. Trained on 5,238 SwissProt proteins under a strict 30% sequence-identity split and using no sequence information, a graph neural network over static MHGs predicts GO molecular function terms across the ontology, demonstrating that vibrational physics alone encodes broad functional class. Kuramoto entrainment of the harmonic coupling graph, formally a Hamiltonian operation over mode frequencies and directly compatible with quantum annealing hardware, improves prediction for proteins whose function depends on collective conformational dynamics. On CLIC1, a fold- and function-switching chloride channel excluded from training, entrainment amplifies channel-activity signal 7.5-fold and antioxidant signal 2.4-fold, recovering both functional states from dynamics alone.

Breast cancer incidence rises with age and peaks across the menopausal transition, yet why some postmenopausal lobules persist, and why that persistence predicts cancer risk, remains unresolved. Incomplete age-related lobular involution is one of the strongest tissue-level predictors of subsequent breast cancer, but it is still commonly viewed as passive failure of hormonally driven regression. This Review proposes a different framework: persistent lobules are maintained by an active reserve niche that outlasts its reproductive function. By integrating breast epidemiology, mammary stromal biology, cellular senescence, immune surveillance, and comparative reserve systems in skeletal muscle, hematopoiesis, and postmenopausal endometrium, we argue that menopause is a biological control point at which tissue fate diverges. Efficient clearance of senescent cells permits lobular regression to complete, whereas impaired immune surveillance may allow inflammatory paracrine signaling, macrophage reprogramming, and immune evasion to create a self-sustaining senescent-immune niche lock. This framework explains why persistent lobules are biologically active, shifts attention from epithelial quantity to microenvironmental state, and identifies the perimenopausal window as a promising interval for biomarker-guided risk stratification and prevention.

Brain encoder models predict cortical fMRI responses from the internal activations of pretrained vision and language networks, and are typically evaluated by held-out prediction accuracy. This is a useful signal for training but a poor one for interpretation: it tells us an encoder fits the data without telling us whether it has internalized the functional organization of the brain. We propose feature visualization -- gradient ascent on the encoder's predicted activation for a target region of interest (ROI) -- as a complementary interpretability technique, and apply it to TRIBE v2 composed with V-JEPA 2 (ViT-G, 40 layers), holding both frozen and synthesizing still images for seven regions spanning the ventral and dorsal visual hierarchies. Under identical hyperparameters, the probe recovers a visible progression of increasing spatial scale and feature complexity across V1 to V4, matching the ventral-stream hierarchy. It also produces three distinctive downstream regimes: radial "frozen-motion" streaks for the middle temporal area (MT) despite static-only optimization, face-like features for the fusiform face area (FFA), and consistent rectilinear line patterns for the parahippocampal place area (PPA). Optimized FFA stimuli drive the predicted region ~4x as much as a natural face photograph, consistent with feature visualization producing adversarial super-stimuli rather than canonical exemplars. The probe is simple, differentiable, and applicable to any brain encoder with a differentiable backbone, allowing for qualitative evaluation of brain encoders.

The striking variety of macroscopic morphologies displayed by bacterial colonies depends on microscopic environmental and behavioural details in a manner that is currently not well understood. A surprising example is sibling inhibition, whereby isogenic bacterial colonies spreading in soft agar hydrogels tend to avoid each other and form sharp demarcation lines when growing nearby. Here we investigate this effect with the common pathogen \textit{Pseudomonas aeruginosa}, by combining quantitative density measurements with a minimal biophysical model. Our results show that the phenomenon does not depend on gel compression, lethal inhibition or quorum sensing-dependent cell communication. Instead, colony separation is driven by localised nutrient depletion through a dynamic feedback between growth and motility. The model, which is calibrated using experimental data, captures key observations including the dependence of inhibition strength on the initial nutrient concentration. This work establishes nutrient availability and non-lethal motility inhibition as central factors underlying sibling inhibition, providing a generalisable framework for microbial spatial dynamics with implications for understanding bacterial interactions in tissues, soils and engineered microbiomes.

Brain-language model comparisons often interpret neural prediction scores as evidence that model representations capture brain-relevant language computation. We asked whether language models align with brains, and whether prediction scores are enough to support that claim, using L-PACT, a source-audited framework that evaluates predictive, relational, mechanism-stripping, and reliability-bounded evidence. Across primary naturalistic language neural datasets and derived language-model representations, L-PACT compared real model features with nuisance baselines and severe controls, tested whether model-to-brain profiles reproduced brain-to-brain patterns, recomputed held-out scores after mechanism stripping, and normalized evidence against brain-brain ceilings. The locked analysis set contains 414 predictive-control rows, 2304 relational profile rows, 4320 mechanism-stripping rows, 420 brain-brain ceiling rows, and 146 integrated decision rows. Assay-sensitivity checks showed that brain-brain reliability, brain-as-model run-to-run relational profiles, independent low-level neural and WAV-derived acoustic-envelope gates, and a deterministic implanted-signal simulation can produce positive evidence when expected. Nevertheless, no real model row passed the predictive, relational, mechanism-stripping, or operational Turing-bounded reliability gates; all 146 integrated rows were control-explained. Less stringent single-criterion rules would have counted raw positive predictive, relational, stripping-delta, and ceiling-normalized effects, but L-PACT downgraded them because controls explained the apparent evidence. In the analyzed derived artifact set, the tested language-model representations do not satisfy L-PACT alignment gates; apparent positives are converted into an auditable control-explained taxonomy rather than treated as structural alignment.

Firing rate fluctuations in neural populations are observed experimentally over multiple time scales, in single neurons, across trials when elicited by stimuli, and across populations. In this work, we examine how firing rate fluctuations emerge in networks of coupled integrate-and-fire neurons as a function of the initial distribution of voltages in networks with time-varying inputs. We analytically derive an approximation for the evolution of the instantaneous population rate or flux as a function of the initial voltage distribution through a Fokker-Planck system. Unlike earlier mean field approaches based on asynchronous or constant flux steady state solutions to the Fokker-Planck system, the approach considered here is based on the transport solution to the advection equation and assumes that the time-varying inputs are slow, and the neurons are in the excitation-driven regime. The transport mean field system predicts how firing rate fluctuations emerge from a dynamic interaction between time-varying inputs, initial densities, and coupling in populations of neurons.

Although recurrent neural networks (RNNs) trained on cognitive tasks have become a widely used framework for studying neural computation, the internal mechanisms by which RNNs switch between rhythms across multiple frequency bands, and how these mechanisms relate to neuronal time constants, have not been systematically analyzed. We trained leaky integrator RNNs with neuron-specific learnable time constants on a four-band (theta, alpha, beta, gamma) rhythm-switching task and analyzed 20 independently trained networks. Whereas low-frequency rhythms were produced by distributed participation of many neurons, high-frequency rhythms were dominated by a small subpopulation of short-time-constant neurons, and the negative correlation between time constant and matched-mode amplitude strengthened monotonically with frequency. Rhythm switching was supported by multiple coexisting mechanisms: turnover of the active subpopulation, network-wide baseline shifts that reposition the operating point near distinct unstable fixed points, and inter-neuronal phase reorganization that selectively cancels or supports band components in the population output. The mechanism deployed for each mode pair varied across training runs, exposing a degeneracy of learned solutions. These findings parallel the coexistence of rhythm-specific and multi-rhythm interneurons reported in biological circuits and provide a candidate framework for interpreting frequency-band-specific functional differentiation in neural systems.

NMR relaxation experiments have shown that there are small but measurable changes in the native state dynamics of the Fyn SH3 domain associated with the substitution by other amino acids of a phenylalanine residue (F20) in the hydrophobic core. We have here used experimental values of NMR order parameters for the wild type protein and two mutational variants (F20L and F20V) as restraints in molecular dynamics simulations. This approach is highly sensitive and provides an atomistic description of the subtle perturbations in native state fluctuations accompanying the mutations. The structural ensembles that we have determined using this method allow the changes in the native state entropy of the protein caused by each of the mutations to be estimated. These entropy changes correspond to free energy variations of several kcal/mol and therefore represent sizable contributions to the overall changes in stability that are associated with the amino acid mutations.

DNA methylation is usually treated as an epigenetic memory mark: transcriptional history is written into regulatory DNA and later stabilizes a chosen cell identity. This picture explains persistence, but it makes memory passive. Here we show that the same promoter-level coupling required for methylation memory can instead turn methylation into an internal control variable for regulatory dynamics. Transcription-factor occupancy protects regulatory DNA from methylation, while methylation shifts later transcription-factor binding thresholds. Under time-scale separation, this reciprocal loop separates into fast expression dynamics conditioned on methylation and a slow methylation flow written by expression. Minimal promoter, self-activation, and fate-toggle models show that this feedback does more than preserve a past state: it autonomously reshapes the expression landscape. In a methylation-coupled toggle, the preferred expression state can move continuously through single-well drift, allowing commitment without first entering a multiwell regime. Stochastic simulations further show that evolving methylation reduces fate reversals relative to a frozen landscape, making weak early expression bias more predictive of later fate. These results recast DNA methylation from a downstream stabilizer of cell identity into a slow dynamical coordinate that can help determine how regulatory states are chosen.

A sufficiently large information flux in recurrent neural networks, quantified by the mutual information between successive network states, is considered a prerequisite for rich information processing capabilities. This raises the question of whether biological neural networks, such as cortical microcolumns, may be structurally organized to enhance information flux. To investigate this possibility, we study a simplified model of the cortical layer 5 architecture, in which a densely and strongly interconnected core population is embedded within a larger supporting network. Surprisingly, we find that the embedding network exerts a pronounced flux-enhancing effect on the core dynamics. Systematic reverse-engineering analyses reveal that the embedding network provides two key contributions: first, it generates effective biases that shift core neurons into a higher-entropy operating regime; second, it supplies stochastic fluctuations that prevent the network from becoming trapped in simple fixed-point or oscillatory attractors through the mechanism of Recurrence Resonance. We further show that the information flux can be increased even beyond the biologically embedded case by applying individually optimized biases to the core neurons, and that these biases can emerge from a simple self-organization principle. Our findings are relevant both for the functional interpretation of biological neural circuits and for the design of artificial recurrent systems such as reservoir computers.

Genome-scale metabolic models (GEMs) are essential tools for systems biology and rational chassis design, but conventional top-down reconstruction depends heavily on sequence homology and often leaves unknown enzymes and metabolic dark matter unresolved. Direct reconstruction from metabolomics is also difficult because mapping observed metabolites to reactions is an ill-posed inverse problem with combinatorial ambiguity and possible spurious networks. Here we present MetaGEM, a bottom-up framework that uses enzymes as physical anchors to convert system-level network inference into enzyme-metabolite interaction prediction. MetaGEM uses a multimodal dual-tower architecture that combines protein evolutionary semantics from a protein language model with three-dimensional metabolite representations. It further introduces contrastive learning with hard negative mining to separate structurally similar metabolites and reduce false positive interactions. On a de-homologized benchmark, MetaGEM achieves state-of-the-art enzyme-metabolite prediction performance, with AUROC of 0.9701 and MCC of 0.8033, and remains robust under low sequence identity splits. In downstream reconstruction, MetaGEM generates functional genome-scale metabolic models for Escherichia coli, Bacillus subtilis, and Pseudomonas aeruginosa. The reconstructed models improve network connectivity, capture promiscuous enzymes, and show strong agreement with experimental phenotype microarray and gene essentiality data. These results indicate that MetaGEM provides a practical route from metabolomic evidence to computable metabolic networks and offers a foundation for automated AI-driven virtual cell reconstruction.

Socio-demographic factors influence social contact patterns and play a fundamental role in shaping the transmission dynamics of infectious diseases. However, compartment-based models of infectious disease dynamics commonly consider the dependence of contact patterns on age, but ignore other factors that are likely to have compounding effects. Methods that stratify the population by multiple socio-demographic factors are few and require social contact surveys that contain information about all factors of interest. Here we present a method that can stratify an existing social contact matrix with an additional socio-demographic factor using information about the population structure of the socio-demographic factors and assumptions about the aggregate mixing rates within and between groups. We then analyse hypothetical populations and a projection of a social contact survey onto Aotearoa New Zealand's age-ethnic structure to show how these extended social contact matrices can change epidemic dynamics and outcomes. The inclusion of the additional factor has a big impact on the model reproduction number and final epidemic size. We find that minority group epidemic outcomes are most sensitive to variation in model parameter values.

Genetic circuit design remains a laborious, expert-driven process despite decades of progress in synthetic biology. We study this problem through code generation: models produce Python code in pysbol3 to construct genetic circuits in the Synthetic Biology Open Language (SBOL), a formal representation that supports automated verification. We introduce GenCircuit-RL, a reinforcement learning framework built around hierarchical verification rewards that decompose correctness into five levels, from code execution to task-specific topological checks, and a four-stage curriculum that shifts optimization pressure from code generation to functional reasoning. We also introduce SynBio-Reason, a benchmark of 4,753 circuits spanning six canonical circuit types and nine tasks from code repair to de novo design, with held-out biological parts for out-of-distribution evaluation. Hierarchical verification improves task success on functional reasoning tasks by 14 to 16 percentage points over binary rewards, and curriculum learning is required for strong design performance. The resulting models generate topologically correct circuits, generalize to novel biological parts, and rediscover canonical designs from the synthetic biology literature.

Spike activity has been the dominant neural signal for behavior decoding due to its high spatial and temporal resolution. However, as brain-computer interfaces (BCIs) move toward high channel counts and wireless operation, the high sampling frequency of spike signals becomes a bottleneck due to high power and bandwidth requirements. Local field potentials (LFPs) represent a different spatial-temporal scale of brain activity compared to spikes, offering key advantages including improved long-term stability, reduced energy consumption, and lower bandwidth requirement. Despite these benefits, LFP-based decoding models typically show reduced accuracy and often rely on non-causal architectures that are unsuitable for real-time deployment. To address these challenges, we propose REALM: a retrospective distillation framework that enables causal LFP decoding. Inspired by offline-to-online distillation strategies in speech recognition, REALM transfers representational knowledge from a pretrained multi-session bidirectional LFP model to a causal version for real-time deployment. We first pretrain a bidirectional Mamba-2 teacher model using a masked autoencoding objective. We then distill this teacher model into a compact student model via a combined objective of representation alignment and task supervision. REALM consistently outperforms both causal and non-causal LFP-based SOTA methods for behavior decoding. Notably, our REALM improves decoding performance while achieving a $2\times$ reduction in parameter count and a $10\times$ reduction in training time. These results demonstrate that retrospective distillation effectively bridges the gap between offline and real-time neural decoding. REALM shows that LFP-only models can achieve competitive decoding performance without reliance on spike signals, offering a practical and scalable alternative for next-generation wireless implantable BCIs.

From subcellular structures to entire organisms, many natural systems generate complex organisation through self-organisation: local interactions that collectively give rise to global structure without any blueprint of the outcome. Yet a significant portion of the information driving such processes is not produced by self-organisation itself, instead, it is often offloaded to initial conditions of the system. Biological development is a prime example, where maternal pre-patterns encode positional and symmetry-breaking information that scaffolds the self-organising process. From maternal morphogen gradients in early embryogenesis to tissue-level morphogenetic pre-patterns guiding organ formation, this transfer of information to initial conditions, analogous to a memory-compute trade-off in computational systems, is a fundamental part of developmental processes. In this work, we study this offloading phenomenon by introducing a model that jointly learns both the self-organisation rules and the pre-patterns, allowing their interplay to be varied and measured under controlled conditions: a Neural Cellular Automaton (NCA) paired with a learned coordinate-based pattern generator (SIREN), both trained simultaneously to generate a set of patterns. We provide information-theoretic analyses of how information is distributed between pre-patterns and the self-organising process, and show that jointly learning both components yields improvements in robustness, encoding capacity, and symmetry breaking over purely self-organising alternatives. Our analysis further suggests that effective pre-patterns do not simply approximate their targets; rather, they bias the developmental dynamics in ways that facilitate convergence, pointing to a non-trivial relationship between the structure of initial conditions and the dynamics of self-organisation.

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros.

Procrastination represents one of the most prevalent behavioral problems associated with individual health and societal productivity. Despite its high prevalence and substantial impact on daily functioning, its underlying neurocognitive mechanisms remain poorly understood. A leading model posits that procrastination arises from imbalanced competing motivations: the avoidance of negative task aversiveness and the pursuit of positive task outcomes, yet this framework has not been fully validated in real-world settings and not applied effectively to guide interventions. Here, we addressed this gap with a double-blind, randomized controlled trial. We applied seven sessions of high-definition transcranial direct current stimulation (HD-tDCS) to the left dorsolateral prefrontal cortex (DLPFC) in chronic procrastinators. Using the intensive experience sampling method (iESM), we assessed the effect of anodal HD-tDCS on real-world procrastination at offline after-effect (2-day interval) and long-term after-effect (6-month follow-up). We found that this neuromodulation produced a lasting reduction in real-world procrastination, with effects sustained at a 6-month follow-up. While the intervention is significantly associated with both decreased task aversiveness and increased perceived task outcome value, a mediation analysis indicated a disassociable mechanism: the increase in task outcome value (but not task aversiveness) showed a statistical pattern consistent with accounting for the observed behavioral improvement. In conclusion, the findings are consistent with the hypothesis that enhancing DLPFC function may reduce procrastination by selectively amplifying the valuation of future rewards, not by simply reducing negative feelings about the task. These results align with established decision-theoretic frameworks and suggest a targeted, theory-informed avenue for future behavioral interventions.

In a context of growing agricultural demand and new challenges related to food security and accessibility, boosting agricultural productivity is more important than ever. Reducing the damage caused by invasive insect species is a crucial lever to achieve this objective. In support of these challenges, and in line with the principles of precision agriculture and Integrated Pest Management (IPM), an innovative simulation framework is presented, aiming to become the digital twin of a pest invasion. Through a flexible rule-based approach of the Agent-Based Modeling (ABM) paradigm, the framework supports the fine-tuning of the main ecological interactions of the pest with its crop host and the environment. Forecasting insect infestation in realistic scenarios, considering both spatial and temporal dimensions, is made possible by integrating heterogeneous data sources: pest biodata collected in the laboratory, environmental data from weather stations, and GIS data of a real crop field. In this study, an application to the global pest of soft fruit, the invasive fruit fly Drosophila suzukii, also known as Spotted Wing Drosophila (SWD), is presented.

Background: Short sequence substrings of a fixed length k, called k-mers, are a ubiquitous computational primitive in bioinformatics, used across sequence indexing, read mapping, genome assembly, metagenomic classification, and comparative genomics. Spaced k-mers generalize this concept by selecting only a subset of positions within a k-mer, improving robustness to mismatches and sequencing errors. While k-mers are computationally highly efficient, spaced k-mers require additional work to be extracted from a sequence, which has slowed down existing methods. Results: We present a collection of efficient algorithms for extracting spaced k-mers from nucleotide sequences, optimized for different hardware architectures. They are based on bit manipulation instructions at CPU level, making them both simpler to implement and up to an order of magnitude faster than existing methods. We further evaluate common pitfalls in k-mer processing, which can cause substantial inefficiencies. Conclusions: Our approaches allow the utilization of spaced k-mers in high-performance bioinformatics applications without major performance degradation compared to regular k-mers, achieving a throughput of up to 750MB of sequence data per second per core. Availability: The implementation in C++20 is published under the MIT license, and freely available at this https URL

We extend the $N$ branching Brownian motions model of population invasion to higher-order asexual reproduction. Increasing reproduction order leads to qualitative changes: invasion fronts generically cease to exist beyond binary reproduction; and in the binary case itself, their speed becomes diffusion-independent. Ternary reproduction shows critical behavior, with collapse into a strongly localized `invasion bullet' in the supercritical regime, diffusive spreading in the subcritical regime, and a continuous family of fronts at criticality. These results suggest that the dominance of division and binary reproduction in nature reflects fundamental constraints on invasion dynamics.

Diffusion-based generative models have reformed generative AI, and also enabled new capabilities in the science domain, e.g., fast generation of 3D structures of molecules. In such tasks, there is often a symmetry in the system, identifying elements that can be converted by certain transformations as equivalent. Equivariant diffusion models guarantee a symmetric distribution, but miss the opportunity to make learning easier, while alignment-based simplification attempts fail to preserve the target distribution. In this work, we develop quotient-space diffusion models, a principled generative framework to fully handle and leverage symmetry. By viewing the intrinsic generation process on the quotient space, the exact construction that removes symmetry redundancy, the framework simplifies learning by allowing model output to have an arbitrary intra-equivalence-class movement, while generating the correct symmetric target distribution with guarantee. We instantiate the framework for molecular structure generation which follows $\mathrm{SE}(3)$ (rigid-body movement) symmetry. It improves the performance over equivariant diffusion models and outperforms alignment-based methods universally for small molecules and proteins, representing a new framework that surpasses previous symmetry treatments in generative models.

To humans, a robin seems more like a bird than a bird seems like a robin, but does this asymmetry also hold for machine vision? Humans and modern vision models can match each other in accuracy while making systematically different kinds of errors, differing not in how often they fail, but in who gets mistaken for whom. We show these directional confusions reveal distinct inductive biases invisible to accuracy alone. Using matched human and deep neural network responses on a natural-image categorization task under 12 perturbation types, we quantify asymmetry in confusion matrices and link its organization to the geometry of the information--error trade-off - how efficiently, and how gracefully, a system generalizes under distortion. We find that humans exhibit broad but weak asymmetries across many class pairs, whereas deep vision models show sparser, stronger directional collapses into a few dominant categories. Robustness training reduces overall asymmetry magnitude but fails to recover this human-like distributed structure. Generative simulations further show that these two asymmetry organizations shift the trade-off geometry in opposite directions even at matched accuracy, explaining why the same scalar asymmetry score can reflect fundamentally different generalization strategies. Together, these results establish directional confusion structure as a sensitive, interpretable signature of inductive bias that accuracy-based evaluation cannot recover.

Existing alignment research is dominated by concerns about safety and preventing harm: safeguards, controllability, and compliance. This paradigm of alignment parallels early psychology's focus on mental illness: necessary but incomplete. What we call Positive Alignment is the development of AI systems that (i) actively support human and ecological flourishing in a pluralistic, polycentric, context-sensitive, and user-authored way while (ii) remaining safe and cooperative. It is a distinct and necessary agenda within AI alignment research. We argue that several existing failures of alignment (e.g., engagement hacking, loss of human autonomy, failures in truth-seeking, low epistemic humility, error correction, lack of diverse viewpoints, and being primarily reactive rather than proactive) may be better addressed through positive alignment, including cultivating virtues and maximizing human flourishing. We highlight a range of challenges, open questions, and technical directions (e.g., data filtering and upsampling, pre- and post-training, evaluations, collaborative value collection) for different phases of the LLM and agents lifecycle. We end with design principles for promoting disagreement and decentralization through contextual grounding, community customization, continual adaptation, and polycentric governance; that is, many legitimate centers of oversight rather than one institutional or moral chokepoint.

EEG microstate analysis segments continuous brain electrical activity into brief, quasi-stable topographic configurations that reflect discrete functional brain states. Conventional approaches such as Modified K-Means operate directly in electrode space with hard assignment, offering no learned latent representation, no generative decoder, and no mechanism to decode latent configurations into verifiable scalp topographies, limiting both model transparency and interpretability. To address this, we present a Convolutional Variational Deep Embedding (Conv-VaDE) model that jointly learns topographic reconstruction and probabilistic soft clustering in a shared latent space. Conv-VaDE enables generative decoding of cluster prototypes into verifiable scalp topographies, replacing opaque hard partitioning with probabilistic soft assignment. A polarity invariance scheme and a four-dimensional grid search over cluster count (K from 3 to 20), latent dimensionality, network depth, and channel width are conducted to systematically reveal how each architectural design choice shapes the quality, stability, and interpretability of learned EEG microstate representations. The model is evaluated on the LEMON resting-state eyes-closed EEG dataset with ten participants using topographic template formation, clustering stability, and global explained variance (GEV). The architecture search reveals that depth L = 4 appears consistently across all 18 best-performing configurations, yielding a best-case GEV of 0.730 and a silhouette of 0.229 at K = 4 across the model sweeps, where moderately deep networks with compact channel widths and small latent dimensionality dominate across the full K range. These results establish that principled architecture search, rather than model scale, is the key to interpretable and stable EEG microstate discovery via variational deep embedding.

Most work in audio enhancement targets human speech, while bioacoustics is less studied due to noisy recordings and the distinct traits of animal sounds. To fill this gap, we adapt speech enhancement methods and build BioSEN, a model made for bioacoustic signals. BioSEN has three modules: a multi-scale dual-axis attention unit for time-frequency feature extraction, a bio-harmonic multi-scale enhancement unit for capturing harmonic structures, and an energy-adaptive gating connection unit that uses frequency weights to keep vocalizations from being removed as noise. Tests on three bioacoustic datasets show that BioSEN matches or exceeds state-of-the-art speech enhancement models while using far less computation. These results show BioSEN's strength for bioacoustic audio enhancement and its promise for biodiversity monitoring and conservation.

Advances in large language models (LLMs) have recently opened new and promising avenues for small-molecule drug discovery. Yet existing LLM-based approaches for molecular generation often suffer from high rates of invalid and low-quality ligand candidates, a result of the syntactic limitations of current models with regard to molecular strings. In this paper, we introduce $\texttt{ToolMol}$, an evolutionary agentic framework for de novo drug design. $\texttt{ToolMol}$ combines a multi-objective genetic algorithm with an agentic LLM operator that iteratively updates the ligand population. We build a comprehensive toolbox of RDKit-backed functions that allows our agentic operator to consisently make precise ligand modifications. $\texttt{ToolMol}$ achieves state-of-the-art performance on multi-objective property optimization tasks, discovering drug-like and synthesizable ligands that have $>10\%$ stronger predicted binding affinity compared to existing methods, evaluated on three protein targets. $\texttt{ToolMol}$ ligands additionally achieve state-of-the-art results in gold-standard Absolute Binding Free Energy scores, gaining over existing methods by over $35\%$. By studying chain-of-thought reasoning traces, we observe that tool-calling enables the model to more faithfully execute its planned modifications, efficiently exploiting the strong chemical prior knowledge in LLMs.