arXiv subjects

Sanjay Jain

Publications and source records attributed to Sanjay Jain.

At least 19 recordsLinked to original sources

arXiv2026

Evaluating Usability in Biomedical Visualization: Rethinking Heuristic Evaluation for Spatial Omics and Multidisciplinary Research Platforms

Introduction: Clinical research informatics (CRI) platforms support biomedical discovery by integrating advanced computational tools into research workflows. Emerging technologies such as spatial omics and AI-enabled imaging expand research capabilities but introduce complex interfaces that increase cognitive burden and alter established analytical processes. Traditional usability frameworks identify general usability issues but often miss challenges specific to high-dimensional biomedical data. Methods: We conducted two complementary studies involving 39 participants to evaluate conventional usability heuristics and identify CRI-specific criteria. Study 1 included 19 undergraduates completing interactive tasks, and Study 2 involved 20 clinical professionals completing an asynchronous hierarchical task framework. Observational and interview data were analyzed using deductive coding based on standard usability heuristics and emerging CRI-specific themes. Results: Simultaneous presentation of complex data overlays and analytical tools overwhelmed users, particularly those with limited spatial-omics experience. Participants relied on trial-and-error exploration and struggled with unlabeled tools in data-rich environments. Feedback indicated that users benefit from phased onboarding, contextual guidance, and progressive feature introduction rather than immediate access to all functionality. Discussion: High-dimensional research platforms require domain-specific usability criteria beyond traditional frameworks. We propose three specialized heuristics: Active Parameter Transparency, Point-of-Use Guidance, and Phased Feature Disclosure. These heuristics help developers manage complexity, provide contextual support, and improve accessibility for multidisciplinary research teams.

cs.HC↗

arXiv2026

New Algorithms for Parity-SAT and Its Bounded-Occurrence Versions

Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT). Under the Strong Exponential Time Hypothesis (SETH), Parity-SAT admits no $O^*((2-\varepsilon)^n)$-time or $O^*((2-\varepsilon)^m)$-time algorithm for any constant $\varepsilon>0$, where $n$ and $m$ denote the numbers of variables and clauses, respectively. Thus, breaking the $2^n$ or $2^m$ barrier appears impossible in full generality. In this work, we revisit this barrier through structural restrictions and a refined exploitation of parity. We study Parity-$d$-occ-SAT, where each variable appears in at most $d$ clauses, and obtain three main results. First, we design a randomized $O^*(2^{m(1-1/O(d))})$-time algorithm, thereby breaking the $2^m$ barrier for every fixed $d$. Second, for the special case $d=2$, we develop a significantly sharper branching algorithm running in $O^*(1.1193^n)$ time or $O^*(1.3248^m)$ time. Third, leveraging the structural insights underlying the $d=2$ case, we obtain an $O^*(1.1052^L)$-time algorithm for general Parity-SAT, where $L$ denotes the formula length. All algorithms use only polynomial space. Notably, our running-time bounds are better than the best known bounds for the corresponding exact counting counterparts, highlighting a genuine algorithmic advantage of parity over counting. Conceptually, our results demonstrate that parity admits finer structural reductions and more efficient branching than exact model counting, and that bounded occurrence can be systematically leveraged to circumvent classical exponential barriers.

cs.DS↗

arXiv2026

A Comprehensive Benchmark of Histopathology Foundation Models for Kidney Digital Pathology Images

Histopathology foundation models (HFMs), pretrained on large-scale cancer datasets, have advanced computational pathology. However, their applicability to non-cancerous chronic kidney disease remains underexplored, despite coexistence of renal pathology with malignancies such as renal cell and urothelial carcinoma. We systematically evaluate 11 publicly available HFMs across 11 kidney-specific downstream tasks spanning multiple stains (PAS, H&E, PASM, and IHC), spatial scales (tile and slide-level), task types (classification, regression, and copy detection), and clinical objectives, including detection, diagnosis, and prognosis. Tile-level performance is assessed using repeated stratified group cross-validation, while slide-level tasks are evaluated using repeated nested stratified cross-validation. Statistical significance is examined using Friedman test followed by pairwise Wilcoxon signed-rank testing with Holm-Bonferroni correction and compact letter display visualization. To promote reproducibility, we release an open-source Python package, kidney-hfm-eval, available at https://pypi.org/project/kidney-hfm-eval/ , that reproduces the evaluation pipelines. Results show moderate to strong performance on tasks driven by coarse meso-scale renal morphology, including diagnostic classification and detection of prominent structural alterations. In contrast, performance consistently declines for tasks requiring fine-grained microstructural discrimination, complex biological phenotypes, or slide-level prognostic inference, largely independent of stain type. Overall, current HFMs appear to encode predominantly static meso-scale representations and may have limited capacity to capture subtle renal pathology or prognosis-related signals. Our results highlight the need for kidney-specific, multi-stain, and multimodal foundation models to support clinically reliable decision-making in nephrology.

cs.CV↗

arXiv2025

Unifying Theories in High-Dimensional Biology: Approaches, Challenges and Opportunities

Across biological subdisciplines, the last decade has seen an explosion of high-dimensional datasets, including datasets for cells, species, immune systems, neurons and behaviour. At the ICTS workshop 'Unifying Theories in High-Dimensional Biophysics' we discussed whether this high dimensionality poses a challenge or opportunity for describing, understanding and predicting biological systems theoretically. We discussed methods, models and frameworks that can help with addressing empirical observations based on these high-dimensional datasets. We summarize the challenges and opportunities that emerged in discussions according to individual participants below.

physics.bio-ph↗

arXiv2025

Vitessce Link: A Mixed Reality and 2D Display Hybrid Approach for Visual Analysis of 3D Tissue Maps

Advances in spatial omics and high-resolution imaging enable the creation of three-dimensional (3D) tissue maps that capture cellular organization and interactions in situ. While these data provide critical insights into tissue function and disease, their exploration is often constrained by tools limited to 2D displays or stereoscopic rendering without analytical integration. We present Vitessce Link, a web-based hybrid framework that unites a 3D stereoscopic view in mixed reality with a synchronized 2D display environment. Users can navigate volumetric data with intuitive hand gestures while controlling channels, filters, and derived data views through the Vitessce platform. Built on open standards and running entirely in the browser, Vitessce Link minimizes friction, supports integration with computational notebooks, and synchronizes interactions across devices via a lightweight WebSocket architecture. Case studies in nephrology and oncology demonstrate how the hybrid approach enhances segmentation evaluation, distance measurement, and interpretation of spatial relationships. Vitessce Link establishes a paradigm for integrative, web-native analysis of 3D tissue maps.

cs.HC↗

arXiv2025

Division Strategies Determine Growth and Viability of Growing-Dividing Autocatalytic Systems

We present a geometric framework to study the growth-division dynamics of cells and protocells, and demonstrate that self-reproduction emerges only when a system's growth dynamics and division strategy are mutually compatible. Using several commonly used models (the linear Hinshelwood cycle and non-linear coarse-grained models of protocells and bacteria), we show that, depending on the chosen division mechanism, the same chemical system can exhibit either (i) balanced exponential growth, (ii) balanced nonexponential growth, or (iii) system death (where the system either diverges to infinity or collapses to zero over successive generations). In particular, we show that cellular trajectories in an N-dimensional phase space (where N is the number of distinct chemical species) shuttle between two N-1 dimensional surfaces - a division surface and a birth surface - and that the relationship between these surfaces and the growth trajectories determine something as fundamental as cellular homeostasis and self-reproduction. Geometrically visualizing bacterial growth and division uncovers, for the first time, the type of division processes that sustain or destroy cellular homeostasis in autocatalytic chemical systems, thereby offering strategies to stabilize or destabilize growing-dividing systems. This reveals that, in addition to autocatalysis of growth, division mechanisms are not passive bystanders but active determinants of a growing-dividing system's long-term fate. Our work thus provides a framework for further exploration of growing dividing systems that will aid in the design of self-reproducing synthetic cells.

nlin.AO↗

arXiv2024

An Improved Algorithm for Sparse Instances of SAT

We show that the CNF satisfiability problem (SAT) can be solved in time $O^*(1.1199^{(d-2)n})$, where $d$ is either the maximum number of occurrences of any variable or the average number of occurrences of all variables if no variable occurs only once. This improves upon the known upper bound of $O^*(1.1279^{(d-2)n})$ by Wahlstr$\ddot{\text{o}}$m (SAT 2005) and $O^*(1.1238^{(d-2)n})$ by Peng and Xiao (IJCAI 2023). For $d\leq 4$, our algorithm is better than previous results. Our main technical result is an algorithm that runs in $O^*(1.1199^n)$ for 3-occur-SAT, a restricted instance of SAT where all variables have at most 3 occurrences. Through deeper case analysis and a reduction rule that allows us to resolve many variables under a relatively broad criteria, we are able to circumvent the bottlenecks in previous algorithms.

cs.DS↗

arXiv2024

Classifying different criteria for learning algebraic structures

In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from a given target family and is required to output an hypothesis about the structure's isomorphism type. So far researchers focused on $\mathbf{Ex}$-learning, in which the learner is asked to eventually stabilize to the correct hypothesis, and on restrictions where the learner is allowed to change the hypothesis a fixed number of times. Yet, other learning paradigms coming from classical algorithmic learning theory remained unexplored. We study the "learning power" of such criteria, comparing them via descriptive-set-theoretic tools thanks to the novel notion of $E$-learnability. The main outcome of this paper is that such criteria admit natural syntactic characterizations in terms of infinitary formulas analogous to the one given for $\mathbf{Ex}$-learning in [6]. Such characterizations give a powerful method to understand whether a family of structure is learnable with respect to the desired criterion.

math.LO↗

arXiv2024

Quasi-Isometric Reductions Between Infinite Strings

This paper studies the recursion-theoretic aspects of large-scale geometries of infinite strings, a subject initiated by Khoussainov and Takisaka (2017). We investigate several notions of quasi-isometric reductions between recursive infinite strings and prove various results on the equivalence classes of such reductions. The main result is the construction of two infinite recursive strings $\alpha$ and $\beta$ such that $\alpha$ is strictly quasi-isometrically reducible to $\beta$, but the reduction cannot be made recursive. This answers an open problem posed by Khoussainov and Takisaka.

cs.FL↗

arXiv2024

Hallucination is Inevitable: An Innate Limitation of Large Language Models

Hallucination has been widely recognized to be a significant drawback for large language models (LLMs). There have been many works that attempt to reduce the extent of hallucination. These efforts have mostly been empirical so far, which cannot answer the fundamental question whether it can be completely eliminated. In this paper, we formalize the problem and show that it is impossible to eliminate hallucination in LLMs. Specifically, we define a formal world where hallucination is defined as inconsistencies between a computable LLM and a computable ground truth function. By employing results from learning theory, we show that LLMs cannot learn all the computable functions and will therefore inevitably hallucinate if used as general problem solvers. Since the formal world is a part of the real world which is much more complicated, hallucinations are also inevitable for real world LLMs. Furthermore, for real world LLMs constrained by provable time complexity, we describe the hallucination-prone tasks and empirically validate our claims. Finally, using the formal world framework, we discuss the possible mechanisms and efficacies of existing hallucination mitigators as well as the practical implications on the safe deployment of LLMs.

cs.CL↗

arXiv2023

Multistable protocells can aid the evolution of prebiotic autocatalytic sets

We present a simple mathematical model that captures the evolutionary capabilities of a prebiotic compartment or protocell. In the model the protocell contains an autocatalytic set whose chemical dynamics is coupled to the growth-division dynamics of the compartment. Bistability in the dynamics of the autocatalytic set results in a protocell that can exist with two distinct growth rates. Stochasticity in chemical reactions plays the role of mutations and causes transitions from one growth regime to another. We show that the system exhibits `natural selection', where a `mutant' protocell in which the autocatalytic set is active arises by chance in a population of inactive protocells, and then takes over the population because of its higher growth rate or `fitness'. The work integrates three levels of dynamics: intracellular chemical, single protocell, and population (or ecosystem) of protocells..

q-bio.PE↗

arXiv2023

Languages given by Finite Automata over the Unary Alphabet

This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the corresponding results. The following main results are obtained: (1) Given two unary NFAs recognising $L$ and $H$, respectively, one can decide whether $L \subseteq H$ as well as whether $L = H$ in time $2^{O((n \log n)^{1/3})}$. The previous upper bound on time was $2^{O((n \log n)^{1/2})}$ as given by Chrobak (1986), and this bound was not significantly improved since then. (2) Given two unary UFAs (unambiguous finite automata) recognising $L$ and $H$, respectively, one can determine a UFA recognising $L \cup H$ and a UFA recognising complement of $L$, where these output UFAs have the number of states bounded by a quasipolynomial in $n$. However, in the worst case, a UFA for recognising concatenation of languages recognised by two $n$-state UFAs, uses $2^{\Theta((n \log^2 n)^{1/3})}$ states. (3) Given a unary language $L$, if $L$ contains the word of length $k$, then let $L(k)=1$ else let $L(k)=0$. Let $\omega_L$ be the $\omega$-word $L(0)L(1)\ldots$ and let $\cal L$ be a fixed $\omega$-regular language. The last section studies how difficult it is to decide, given an $n$-state UFA or NFA

cs.FL↗

arXiv2023

String Compression in FA-Presentable Structures

We construct a FA-presentation $ψ: L \rightarrow \mathbb{N}$ of the structure $(\mathbb{N};\mathrm{S})$ for which a numerical characteristic $r(n)$ defined as the maximum number $ψ(w)$ for all strings $w \in L$ of length less than or equal to $n$ grows faster than any tower of exponents of a fixed height. This result leads us to a more general notion of a compressibility rate defined for FA-presentations of any FA-presentable structure. We show the existence of FA-presentations for the configuration space of a Turing machine and Cayley graphs of some groups for which it grows faster than any tower of exponents of a fixed height. For FA-presentations of the Presburger arithmetic $(\mathbb{N};+)$ we show that it is bounded from above by a linear function.

cs.FL↗

arXiv2022

Addition Machines, Automatic Functions and Open Problems of Floyd and Knuth

Floyd and Knuth investigated in 1990 register machines which can add, subtract and compare integers as primitive operations. They asked whether their current bound on the number of registers for multiplying and dividing fast (running in time linear in the size of the input) can be improved and whether one can output fast the powers of two summing up to a positive integer in subquadratic time. Both questions are answered positively. Furthermore, it is shown that every function computed by only one register is automatic and that automatic functions with one input can be computed with four registers in linear time; automatic functions with a larger number of inputs can be computed with 5 registers in linear time. There is a nonautomatic function with one input which can be computed with two registers in linear time.

cs.CC↗

arXiv2022

Alternating Automatic Register Machines

This paper introduces and studies a new model of computation called an Alternating Automatic Register Machine (AARM). An AARM possesses the basic features of a conventional register machine and an alternating Turing machine, but can carry out computations using bounded automatic relations in a single step. One finding is that an AARM can recognise some NP-complete problems, including SAT (using a particular coding), in $\log^* n + O(1)$ steps. On the other hand, if all problems in P can be solved by an AARM in $O(\log^*n)$ rounds, then $\text{P} \subset \text{PSPACE}$. Furthermore, we study an even more computationally powerful machine, called a Polynomial-Size Padded Alternating Automatic Register Machine (PAARM), which allows the input to be padded with a polynomial-size string. It is shown that the polynomial hierarchy can be characterised as the languages that are recognised by a PAARM in $\log^*n + O(1)$ steps. These results illustrate the power of alternation when combined with computations involving automatic relations, and uncover a finer gradation between known complexity classes.

cs.CC↗

arXiv2022

A Computation Model with Automatic Functions and Relations as Primitive Operations

Prior work of Hartmanis and Simon (Hartmanis and Simon, 1974) and Floyd and Knuth (Floyd and Knuth, 1990) investigated what happens if a device uses primitive steps more natural than single updates of a Turing tape. One finding was that in the numerical setting, addition, subtraction, comparisons and bit-wise Boolean operations of numbers preserve polynomial time while incorporating concatenation or multiplication allows to solve all PSPACE problems in polynomially many steps. Therefore we propose to use updates and comparisons with automatic functions as primitive operations and use constantly many registers; the resulting model covers all primitive operations of Hartmanis and Simon as well as Floyd and Knuth, but the model remains in polynomial time. The present work investigates in particular the deterministic complexity of various natural problems and also gives an overview on the nondeterministic complexity of this model.

cs.CC↗

arXiv2021

Learnability and Positive Equivalence Relations

Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into infinitely many equivalence classes. The present work investigates the infinite one-one numbered recursively enumerable (r.e.) families realised by such relations and asks how the choice of the equivalence relation impacts the learnability properties of these classes when studying learnability in the limit from positive examples, also known as learning from text. For all choices of such positive equivalence relations, for each of the following entries, there are one-one numbered r.e. families which satisfy it: (a) they are behaviourally correctly learnable but not vacillatorily learnable; (b) they are explanatorily learnable but not confidently learnable; (c) they are not behaviourally correctly learnable. Furthermore, there is a positive equivalence relation which enforces that (d) every vacillatorily learnable one-one numbered family of languages closed under this equivalence relation is already explanatorily learnable and cannot be confidently learnable.

cs.LO↗

arXiv2021

Ordered Semiautomatic Rings with Applications to Geometry

The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and transformations are automatic. The underlying ring has always to be a countable dense subring of the real numbers and additions and comparisons and multiplications with constants need to be automatic. It is shown that the ring can be selected such that equilateral triangles can be represented and rotations by 30 degrees are possible, while the standard representation of the b-adic rationals does not allow this.

cs.FL↗