arXiv subjects

Sanjay Jain

Publications and source records attributed to Sanjay Jain.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2020

Capsules for Biomedical Image Segmentation

Our work expands the use of capsule networks to the task of object segmentation for the first time in the literature. This is made possible via the introduction of locally-constrained routing and transformation matrix sharing, which reduces the parameter/memory burden and allows for the segmentation of objects at large resolutions. To compensate for the loss of global information in constraining the routing, we propose the concept of "deconvolutional" capsules to create a deep encoder-decoder style network, called SegCaps. We extend the masked reconstruction regularization to the task of segmentation and perform thorough ablation experiments on each component of our method. The proposed convolutional-deconvolutional capsule network, SegCaps, shows state-of-the-art results while using a fraction of the parameters of popular segmentation networks. To validate our proposed method, we perform experiments segmenting pathological lungs from clinical and pre-clinical thoracic computed tomography (CT) scans and segmenting muscle and adipose (fat) tissue from magnetic resonance imaging (MRI) scans of human subjects' thighs. Notably, our experiments in lung segmentation represent the largest-scale study in pathological lung segmentation in the literature, where we conduct experiments across five extremely challenging datasets, containing both clinical and pre-clinical subjects, and nearly 2000 computed-tomography scans. Our newly developed segmentation platform outperforms other methods across all datasets while utilizing less than 5% of the parameters in the popular U-Net for biomedical image segmentation. Further, we demonstrate capsules' ability to generalize to unseen rotations/reflections on natural images.

eess.IV↗

arXiv2020

Construction and Usage of a Human Body Common Coordinate Framework Comprising Clinical, Semantic, and Spatial Ontologies

The National Institutes of Health's (NIH) Human Biomolecular Atlas Program (HuBMAP) aims to create a comprehensive high-resolution atlas of all the cells in the healthy human body. Multiple laboratories across the United States are collecting tissue specimens from different organs of donors who vary in sex, age, and body size. Integrating and harmonizing the data derived from these samples and 'mapping' them into a common three-dimensional (3D) space is a major challenge. The key to making this possible is a 'Common Coordinate Framework' (CCF), which provides a semantically annotated, 3D reference system for the entire body. The CCF enables contributors to HuBMAP to 'register' specimens and datasets within a common spatial reference system, and it supports a standardized way to query and 'explore' data in a spatially and semantically explicit manner. [...] This paper describes the construction and usage of a CCF for the human body and its reference implementation in HuBMAP. The CCF consists of (1) a CCF Clinical Ontology, which provides metadata about the specimen and donor (the 'who'); (2) a CCF Semantic Ontology, which describes 'what' part of the body a sample came from and details anatomical structures, cell types, and biomarkers (ASCT+B); and (3) a CCF Spatial Ontology, which indicates 'where' a tissue sample is located in a 3D coordinate system. An initial version of all three CCF ontologies has been implemented for the first HuBMAP Portal release. It was successfully used by Tissue Mapping Centers to semantically annotate and spatially register 48 kidney and spleen tissue blocks. The blocks can be queried and explored in their clinical, semantic, and spatial context via the CCF user interface in the HuBMAP Portal.

q-bio.QM↗

arXiv2020

A Faster Exact Algorithm to Count X3SAT Solutions

The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are set to 0. If we restrict the length of each clause to be at most 3 literals, then it is known as the X3SAT problem. In this paper, we consider the problem of counting the number of satisfying assignments to the X3SAT problem, which is also known as #X3SAT. The current state of the art exact algorithm to solve #X3SAT is given by Dahllöf, Jonsson and Beigel and runs in $O(1.1487^n)$, where $n$ is the number of variables in the formula. In this paper, we propose an exact algorithm for the #X3SAT problem that runs in $O(1.1120^n)$ with very few branching cases to consider, by using a result from Monien and Preis to give us a bisection width for graphs with at most degree 3.

cs.DS↗

arXiv2020

Neural Network Segmentation of Interstitial Fibrosis, Tubular Atrophy, and Glomerulosclerosis in Renal Biopsies

Glomerulosclerosis, interstitial fibrosis, and tubular atrophy (IFTA) are histologic indicators of irrecoverable kidney injury. In standard clinical practice, the renal pathologist visually assesses, under the microscope, the percentage of sclerotic glomeruli and the percentage of renal cortical involvement by IFTA. Estimation of IFTA is a subjective process due to a varied spectrum and definition of morphological manifestations. Modern artificial intelligence and computer vision algorithms have the ability to reduce inter-observer variability through rigorous quantitation. In this work, we apply convolutional neural networks for the segmentation of glomerulosclerosis and IFTA in periodic acid-Schiff stained renal biopsies. The convolutional network approach achieves high performance in intra-institutional holdout data, and achieves moderate performance in inter-intuitional holdout data, which the network had never seen in training. The convolutional approach demonstrated interesting properties, such as learning to predict regions better than the provided ground truth as well as developing its own conceptualization of segmental sclerosis. Subsequent estimations of IFTA and glomerulosclerosis percentages showed high correlation with ground truth.

q-bio.TO↗

arXiv2019

A Fast Exponential Time Algorithm for Max Hamming Distance X3SAT

X3SAT is the problem of whether one can satisfy a given set of clauses with up to three literals such that in every clause, exactly one literal is true and the others are false. A related question is to determine the maximal Hamming distance between two solutions of the instance. Dahllöf provided an algorithm for Maximum Hamming Distance XSAT, which is more complicated than the same problem for X3SAT, with a runtime of $O(1.8348^n)$; Fu, Zhou and Yin considered Maximum Hamming Distance for X3SAT and found for this problem an algorithm with runtime $O(1.6760^n)$. In this paper, we propose an algorithm in $O(1.3298^n)$ time to solve the Max Hamming Distance X3SAT problem; the algorithm actually counts for each $k$ the number of pairs of solutions which have Hamming Distance $k$.

cs.CC↗

arXiv2019

The Science of Murray Gell-Mann

This article summarizes some of the most important scientific contributions of Murray Gell-Mann (1929-2019). (Invited article for Current Science, Indian Academy of Sciences.)

physics.hist-ph↗

arXiv2019

The isomorphism problem for tree-automatic ordinals with addition

This paper studies tree-automatic ordinals (or equivalently, well-founded linearly ordered sets) together with the ordinal addition operation +. Informally, these are ordinals such that their elements are coded by finite trees for which the linear order relation of the ordinal and the ordinal addition operation can be determined by tree automata. We describe an algorithm that, given two tree-automatic ordinals with the ordinal addition operation, decides if the ordinals are isomorphic.

cs.FL↗

arXiv2019

Random Subgroups of Rationals

This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of $(G,+)$; second, what learnability properties can one extract from $G$ and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of $(G,+)$ coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for $G$ with respect to any generating sequence for $G$ is not even semi-decidable, one can build a generating sequence $β$ such that the word problem for $G$ with respect to $β$ is co-recursively enumerable (assuming that the set of generators of $G$ is limit-recursive). In regard to the second question, it is proven that there is a generating sequence $β$ for $G$ such that every non-trivial finitely generated subgroup of $G$ is recursively enumerable and the class of all such subgroups of $G$ is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of $G$ is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of $G$ cannot be syntactically identified in the limit with respect to any generating sequence for $G$. The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.

cs.LO↗

arXiv2018

Iterative annotation to ease neural network training: Specialized machine learning in medical image analysis

Neural networks promise to bring robust, quantitative analysis to medical fields, but adoption is limited by the technicalities of training these networks. To address this translation gap between medical researchers and neural networks in the field of pathology, we have created an intuitive interface which utilizes the commonly used whole slide image (WSI) viewer, Aperio ImageScope (Leica Biosystems Imaging, Inc.), for the annotation and display of neural network predictions on WSIs. Leveraging this, we propose the use of a human-in-the-loop strategy to reduce the burden of WSI annotation. We track network performance improvements as a function of iteration and quantify the use of this pipeline for the segmentation of renal histologic findings on WSIs. More specifically, we present network performance when applied to segmentation of renal micro compartments, and demonstrate multi-class segmentation in human and mouse renal tissue slides. Finally, to show the adaptability of this technique to other medical imaging fields, we demonstrate its ability to iteratively segment human prostate glands from radiology imaging data.

eess.IV↗

arXiv2018

Feedbacks from the metabolic network to the genetic network reveal regulatory modules in E. coli and B. subtilis

The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.

q-bio.MN↗

arXiv2018

An Ordered Approach to Solving Parity Games in Quasi Polynomial Time and Quasi Linear Space

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their data structure as a progress measure, allowing for a backward implementation instead of a complete unravelling of the game. To achieve this, a number of changes have to be made to their techniques, where the main one is to add power to the antagonistic player that allows for determining her rational move without changing the outcome of the game. We provide a first implementation for a quasi-polynomial algorithm, test it on small examples, and provide a number of side results, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al.

cs.LO↗

arXiv2017

Multi-radial LBP Features as a Tool for Rapid Glomerular Detection and Assessment in Whole Slide Histopathology Images

We demonstrate a simple and effective automated method for the segmentation of glomeruli from large (~1 gigapixel) histopathological whole-slide images (WSIs) of thin renal tissue sections and biopsies, using an adaptation of the well-known local binary patterns (LBP) image feature vector to train a support vector machine (SVM) model. Our method offers high precision (>90%) and reasonable recall (>70%) for glomeruli from WSIs, is readily adaptable to glomeruli from multiple species, including mouse, rat, and human, and is robust to diverse slide staining methods. Using 5 Intel(R) Core(TM) i7-4790 CPUs with 40 GB RAM, our method typically requires ~15 sec for training and ~2 min to extract glomeruli reproducibly from a WSI. Deploying a deep convolutional neural network trained for glomerular recognition in tandem with the SVM suffices to reduce false positives to below 3%. We also apply our LBP-based descriptor to successfully detect pathologic changes in a mouse model of diabetic nephropathy. We envision potential clinical and laboratory applications for this approach in the study and diagnosis of glomerular disease, and as a means of greatly accelerating the construction of feature sets to fuel deep learning studies into tissue structure and pathology.

q-bio.TO↗

arXiv2016

How to verify computation with a rational network

The present paper introduces a practical protocol for provably secure, outsourced computation. Our protocol minimizes overhead for verification by requiring solutions to withstand an interactive game between a prover and challenger. For optimization problems, the best or nearly best of all submitted solutions is expected to be accepted by this approach. Financial incentives and deposits are used in order to overcome the problem of fake participants.

cs.GT↗

arXiv2013

Automatic functions, linear time and learning

The present work determines the exact nature of {\em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time notions permit full learnability for learning in the limit of automatic classes (families of languages which are uniformly recognised by a finite automaton). In particular it is shown that a function is automatic iff there is a one-tape Turing machine with a left end which computes the function in linear time where the input before the computation and the output after the computation both start at the left end. It is known that learners realised as automatic update functions are restrictive for learning. In the present work it is shown that one can overcome the problem by providing work tapes additional to a resource-bounded base tape while keeping the update-time to be linear in the length of the largest datum seen so far. In this model, one additional such work tape provides additional learning power over the automatic learner model and two additional work tapes give full learning power. Furthermore, one can also consider additional queues or additional stacks in place of additional work tapes and for these devices, one queue or two stacks are sufficient for full learning power while one stack is insufficient.

cs.FL↗

arXiv2012

Flux-based classification of reactions reveals a functional bow-tie organization of complex metabolic networks

Unraveling the structure of complex biological networks and relating it to their functional role is an important task in systems biology. Here we attempt to characterize the functional organization of the large-scale metabolic networks of three microorganisms. We apply flux balance analysis to study the optimal growth states of these organisms in different environments. By investigating the differential usage of reactions across flux patterns for different environments, we observe a striking bimodal distribution in the activity of reactions. Motivated by this, we propose a simple algorithm to decompose the metabolic network into three sub-networks. It turns out that our reaction classifier which is blind to the biochemical role of pathways leads to three functionally relevant sub-networks that correspond to input, output and intermediate parts of the metabolic network with distinct structural characteristics. Our decomposition method unveils a functional bow-tie organization of metabolic networks that is different from the bow-tie structure determined by graph-theoretic methods that do not incorporate functionality.

q-bio.MN↗