The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on the surfaces embedded in three-dimensional Euclidean space by using exterior differential forms.

This work aims at showing the relevance and the applications possibilities of the Fibonacci sequence, and also its q-deformed or quantum extension, in the study of the genetic code(s). First, after the presentation of a new formula, an indexed double Fibonacci sequence, comprising the first six Fibonacci numbers, is shown to describe the 20 amino acids multiplets and their degeneracy as well as a characteristic pattern for the 61 meaningful codons. Next, the twenty amino acids, classified according to their increasing atom-number (carbon, nitrogen, oxygen and sulfur), exhibit several Fibonacci sequence patterns. Several mathematical relations are given, describing various atom-number patterns. Finally, a q-Fibonacci simple phenomenological model, with q a real deformation parameter, is used to describe, in a unified way, not only the standard genetic code, when q=1, but also all known slight variations of this latter, when q~1, as well as the case of the 21st amino acid (Selenocysteine) and the 22nd one (Pyrrolysine), also when q~1. As a by-product of this elementary model, we also show that, in the limit q=0, the number of amino acids reaches the value 6, in good agreement with old and still persistent claims stating that life, in its early development, could have used only a small number of amino acids.

Accelerating the discovery of novel and more effective therapeutics is an important pharmaceutical problem in which deep learning is playing an increasingly significant role. However, real-world drug discovery tasks are often characterized by a scarcity of labeled data and significant covariate shift$\unicode{x2013}\unicode{x2013}$a setting that poses a challenge to standard deep learning methods. In this paper, we present Q-SAVI, a probabilistic model able to address these challenges by encoding explicit prior knowledge of the data-generating process into a prior distribution over functions, presenting researchers with a transparent and probabilistically principled way to encode data-driven modeling preferences. Building on a novel, gold-standard bioactivity dataset that facilitates a meaningful comparison of models in an extrapolative regime, we explore different approaches to induce data shift and construct a challenging evaluation setup. We then demonstrate that using Q-SAVI to integrate contextualized prior knowledge of drug-like chemical space into the modeling process affords substantial gains in predictive accuracy and calibration, outperforming a broad range of state-of-the-art self-supervised pre-training and domain adaptation techniques.

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the reasoning that is intrinsic of the theory does not appear in the length of proofs. In general, the congruence is defined through a rewrite system over terms and propositions. We define a rigorous framework to study proof lengths in deduction modulo, where the congruence must be computed in polynomial time. We show that even very simple rewrite systems lead to arbitrary proof-length speed-ups in deduction modulo, compared to using axioms. As higher-order logic can be encoded as a first-order theory in deduction modulo, we also study how to reinterpret, thanks to deduction modulo, the speed-ups between higher-order and first-order arithmetics that were stated by Gödel. We define a first-order rewrite system with a congruence decidable in polynomial time such that proofs of higher-order arithmetic can be linearly translated into first-order arithmetic modulo that system. We also present the whole higher-order arithmetic as a first-order system without resorting to any axiom, where proofs have the same length as in the axiomatic presentation.

We survey the emerging area of compression-based, parameter-free, similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a certain precision for that family if it minorizes every distance in the family between every two objects in the set, up to the stated precision (we do not require the universal distance to be an element of the family). We consider similarity distances for two types of objects: literal objects that as such contain all of their meaning, like genomes or books, and names for objects. The latter may have literal embodyments like the first type, but may also be abstract like ``red'' or ``christianity.'' For the first type we consider a family of computable distance measures corresponding to parameters expressing similarity according to particular featuresdistances generated by web users corresponding to particular semantic relations between the (names for) the designated objects. For both families we give universal similarity distance measures, incorporating all particular distance measures in the family. In the first case the universal distance is based on compression and in the second case it is based on Google page counts related to search terms. In both cases experiments on a massive scale give evidence of the viability of the approaches. between pairs of literal objects. For the second type we consider similarity

Recent advances in generative recommenders adopt a two-stage paradigm: items are first tokenized into semantic IDs using a pretrained tokenizer, and then large language models (LLMs) are trained to generate the next item via sequence-to-sequence modeling. However, these two stages are optimized for different objectives: semantic reconstruction during tokenizer pretraining versus user interaction modeling during recommender training. This objective misalignment leads to two key limitations: (i) suboptimal static tokenization, where fixed token assignments fail to reflect diverse usage contexts; and (ii) discarded pretrained semantics, where pretrained knowledge - typically from language model embeddings - is overwritten during recommender training on user interactions. To address these limitations, we propose to learn $\underline{DE}$composed $\underline{CO}$ntextual Token $\underline{R}$epresentations (DECOR), a unified framework that preserves pretrained semantics while enhancing the adaptability of token embeddings. DECOR introduces contextualized token composition to refine token embeddings based on user interaction context, and decomposed embedding fusion that integrates pretrained codebook embeddings with newly learned collaborative embeddings. Experiments on three real-world datasets demonstrate that DECOR consistently outperforms state-of-the-art baselines in recommendation performance.

This work first presents our attempts to establish an automated model using state-of-the-art approaches for analysing bias in search results of Bing and Google. Experimental results indicate that the current class-wise F1-scores of our best model are not sufficient to establish an automated model for bias analysis. Thus, we decided not to continue with this approach.

We present a minimal model to study liquid phase separation in a fixed pH ensemble. The model describes a mixture composed of macromolecules that exist in three different charge states and have a tendency to phase separate. We introduce the pH dependence of phase separation by means of a set of reactions describing the protonation and deprotonation of macromolecules, as well as the self-ionisation of water. We use conservation laws to identify the conjugate thermodynamic variables at chemical equilibrium. Using this thermodynamic conjugate variables we perform a Legendre transform which defines the corresponding free energy at fixed pH. We first study the possible phase diagram topologies at the isoelectric point of the macromolecules. We then show how the phase behavior depends on pH by moving away from the isoelectric point. We find that phase diagrams as a function of pH strongly depend on whether oppositely charged macromolecules or neutral macromolecules have a stronger tendency to phase separate. We predict the existence of reentrant behavior as a function of pH. In addition, our model also predicts that the region of phase separation is typically broader at the isoelectric point. This model could account for both, the protein separation observed in yeast cells for pH values close to the isoelectric point of many cytosolic proteins and also for the in vitro experiments of single proteins exhibiting phase separation as a function of pH.

This study reveals the essence of ligand recognition mechanisms by which calmodulin (CaM) controls a variety of Ca2+ signaling processes. We study eight forms of calcium-loaded CaM each with distinct conformational states. Reducing the structure to two degrees of freedom conveniently describes main features of conformational changes of CaM via simultaneous twist-bend motions of the two lobes. We utilize perturbation-response scanning (PRS) technique, coupled with molecular dynamics simulations to analyze conformational preferences of calcium-loaded CaM, initially in extended form. PRS is comprised of sequential application of directed forces on residues followed by recording the resulting coordinates. We show that manipulation of a single residue, E31 located in one of the EF hand motifs, reproduces structural changes to compact forms, and the flexible linker acts as a transducer of binding information to distant parts of the protein. Independently, using four different pKa calculation strategies, we find E31 to be the charged residue (out of 52), whose ionization state is most sensitive to subtle pH variations in the physiological range. It is proposed that at relatively low pH, CaM structure is less flexible. By gaining charged states at specific sites at a pH value around 7, local conformational changes in the protein will lead to shifts in the energy landscape, paving the way to other conformational states. These findings are in accordance with FRET measured shifts in conformational distributions towards more compact forms with decreased pH. They also corroborate mutational studies and proteolysis results which point to the significant role of E31 in CaM dynamics.

Many networked systems require a central authority to enforce a global configuration against local peer influence. We study influence dynamics on finite weighted directed graphs with a distinguished hub node and binary vertex states ('Glory' or 'Gnash'). We give a sharp, local, and efficiently checkable criterion that guarantees global convergence to Glory in a single synchronous update from any initial state. At each non-hub vertex, the incoming weight from the hub must at least match the total incoming weight from all other nodes. Specialising in uniform hub broadcasts, the exact threshold equals the maximum non-hub incoming weight over all vertices, and we prove this threshold is tight. We extend the result to a tau-biased update rule and to asynchronous (Gauss-Seidel) schedules, where a single pass still suffices under the same domination hypothesis. Machine-checked proofs in Coq accompany all theorems.