קולוקוויום וסמינרים

Self-Organizing Maps are unsupervised machine learning algorithms used primarily for clustering and dimensionality reduction. They map high-dimensional data for improved interpretability using a competitive learning approach. Each data point is mapped with some distance to a point on the map. These distances, called activations, show underlying trajectories in the data that can be explored. This is done in two studies.

The first study seeks vulnerabilities in public data by using self-organizing maps to bring people's sensitive attributes to the surface. This can reveal sensitive attributes with low correlation to the data are recoverable, thus leaving people's personal data at risk.

The second study looks into finding underlying trajectories in cell types. Cell type trajectory inference, also called pseudotime analysis, maps developmental and state changes in cells. Using trajectory inference to order single-cell omics data is used in stem cell differentiation, disease progression, and cell response to stimuli among other things.

These studies open the door to new research into applications of self-organizing maps from a 3rd dimension.

Koopman-based methods for time-series forecasting model nonlinear dynamics as linear evolution in a latent space, but deterministic formulations often mix noise with the underlying dynamics, limiting long-term accuracy. This talk introduces KoopSDE, which extends Koopman models with a latent stochastic differential equation.

By linking the drift to the Koopman generator and learning a diffusion term, the method separates dynamics from noise and improves robustness in long-horizon forecasting.

The adaptation of Large Language Model architectures to computational biology has enabled Single-Cell Foundation Models for learning from single-cell RNA-sequencing data. However, many of these models rely on masking strategies from natural language processing; unlike words in a sentence, gene expression is governed by highly correlated regulatory networks, making random masking or structure naive techniques biologically misaligned. Viewed through an information-theoretic lens, this introduces a key inefficiency: models can reconstruct masked genes from local correlations, limiting their ability to learn accurate biological representations based on higher-order structure and driving reliance on large datasets - a challenge in data-scarce settings such as rare disease cohorts or privacy-preserving environments.

To address this, we introduce domain-informed masking during pre-training. In this talk, we present CorrMask, a data-driven, dependency-aware masking scheme that leverages gene correlation structure to jointly mask related genes, encouraging learning from global cellular context. Across tissue-specific datasets, CorrMask matches baseline performance on both cell- and gene-level tasks using less data, with the strongest gains in underrepresented cell populations.

These results position CorrMask as an effective “data multiplier” for enabling efficient, biologically grounded foundation models, with broader implications for predictive modeling in our field.

We consider the Minimum Linear Ordering Problem: given a ground set N of cardinality n and a non-negative set function f: 2^N→R≥0, the goal is to find an ordering π of N that minimizes the sum of the values of f over all prefixes of π. This problem has been studied for various classes of set functions, and the case of a submodular f is of special interest, as it captures classic problems including Minimum Linear Arrangement and Minimum Containing Interval Graph. In this work, we resolve the approximability of the Minimum Linear Ordering Problem for a general submodular f by establishing matching upper and lower bounds and present: (1) a polynomial-time algorithm achieving an O(√(n/ln n))-approximation; and (2) a matching information-theoretic hardness result, showing that no algorithm evaluating f a polynomial number of times can achieve an o(√(n/ln n))-approximation. Previously, the best known hardness of approximation was 2, and an O(√(n/ln n))-approximation was known only for the special case where f is both submodular and symmetric.

Task Assistance Planning (TAP) involves coordinating an assisting robot to support a task robot executing a predefined trajectory, with the goal of maximizing the duration of effective assistance to the task robot. This coordination may be critical in diverse applications such as providing a communication relay in search-and-rescue missions. While existing approaches optimally solve TAP on static, precomputed discrete roadmaps, they scale poorly to continuous configuration spaces because committing to a fixed roadmap can either omit optimal solutions or incur prohibitive preprocessing delays. Furthermore, a naive anytime extension that interleaves continuous roadmap densification with optimal discrete solvers introduces cyclic temporal dependencies that render the problem computationally intractable. To address this gap, we introduce Directed Acyclic Roadmap for TAP (DART), an anytime algorithmic framework designed for continuous TAP. DART restricts the incrementally constructed roadmap to a Directed Acyclic Graph (DAG). This key architectural shift eliminates cyclic temporal dependencies, drastically reducing the combinatorial search space evaluated during path optimization. We evaluate DART on both low-dimentional simulated real-world problem and high-dimentional synthetic problem and demonstrate empirically that DART achieves computational speedups of up to three orders of magnitude compared to undirected baseline methods, allowing for rapid incremental updates and the discovery of higher-quality assistance trajectories within a given time budget.

Proteins are fundamental to biological systems, and accurately representing them is essential for understanding biological function and drug discovery. Recent protein language models learn representations from amino acid sequences, yet proteins are inherently multidimensional, characterized by structure, dynamics, and molecular interactions. This thesis investigates how integrating multidimensional protein knowledge can enhance protein language models and improve biological understanding.

We introduce GOProteinGNN for integrating protein knowledge graphs, FusionProt for sequence–structure fusion, ProtLigand for leveraging protein–ligand interactions, and DynamicsPLM for modeling conformational dynamics. Across diverse biological tasks, these approaches improve performance and produce biologically meaningful representations.

This research was also applied in a drug discovery laboratory, demonstrating the practical value of multidimensional protein representations. Overall, this thesis shows that integrating functional, structural, dynamic, and interaction-based information substantially enhances protein representation learning and supports advances in biomedical research.

We introduce the sum channel, a new channel model motivated by applications in distributed storage and DNA data storage. In the error-free case, it takes as input an $\ell$-row binary matrix and outputs an $(\ell+1)$-row matrix whose first $\ell$ rows equal the input and whose last row is their parity (sum) row.

We construct a two-deletion-correcting code with redundancy $2\lceil\log_2\log_2 n\rceil+ \log_2 \ell + O(1)$ for $\ell$-row inputs. When $\ell=2$, we establish a lower bound of $\lceil\log_2\log_2 n\rceil + O(1)$ bits, implying that our redundancy is optimal up to a factor of 2.

We also present a code correcting a single substitution with $\lceil \log_2(\ell+1)\rceil$ redundant bits and prove that it is within one bit of optimality.

A "named page" is a memory page whose content originates from and is backed by a file. Because named pages are regularly read from and written to persistent storage, filesystems strive to preserve file content contiguity, thereby enabling sequential I/O, which can be much faster than random I/O. No analogous effort to preserve contiguity exists for "anonymous pages," which hold unnamed data such as stack or heap bytes. Consequently, swapping a region of anonymous pages in or out can be much slower than reading or writing a region of named pages.

We observe (1) that the main advantage of the existing swap mechanism is high swap area utilization, since any anonymous page can be placed at any offset within the swap file, so there is no fragmentation; but (2) that secondary storage is commonly underutilized, so the cost of random I/O may be unwarranted. We therefore propose "named swapping," which associates each anonymous region with its own (swap) file and thus benefits from the underlying filesystem's efforts to maintain contiguity, improving swap performance by up to an order of magnitude. A key challenge we address is anonymous pages shared across multiple regions due to fork-based copy-on-write.