• First AFNO-based spectral mixing for 3D medical segmentation • Eliminates quadratic token-to-token attention entirely • Linear memory scaling for high-resolution 3D volumes • 78% fewer parameters than UNETR++ • SOTA or near-SOTA on ACDC, Synapse, and BraTS We adapt the remote sensing-inspired AMBER model (Dosi et al., 2025) from multi-band image segmentation to 3D medical datacube segmentation. To address the computational bottleneck of the volumetric transformer, we propose the AMBER-AFNO architecture. This approach uses Adaptive Fourier Neural Operators (AFNO) instead of the multi-head self-attention mechanism. Unlike spatial pairwise interactions between tokens, global token mixing in the frequency domain avoids O ( N 2 ) attention-weight calculations. As a result, AMBER-AFNO achieves quasi-linear computational complexity and linear memory scaling. This new way to model global context reduces reliance on dense transformers while preserving global contextual modeling capability. By using attention-free spectral operations, our design offers a compact parameterization and maintains a competitive computational complexity. We evaluate AMBER-AFNO on three public datasets: ACDC, Synapse, and BraTS. On these datasets, the model achieves state-of-the-art or near-state-of-the-art results for DSC and HD95. Compared with recent compact CNN and Transformer architectures, our approach yields higher Dice scores while maintaining a compact model size. Overall, our results show that frequency-domain token mixing with AFNO provides a fast and efficient alternative to self-attention mechanisms for 3D medical image segmentation.

Nowadays, Human Activity Recognition (HAR) is growing in interest considering the widespread adoption of cheap and healthcare-based devices like Inertial Measurement Units (IMUs) or smartwatches. This study introduces three key advancements in HAR in the context of sports performance monitoring: (i) the development of a stretchable-sensor-based dataset comprising five individuals performing walking, jogging, and running; (ii) the design of an ultra-lightweight image encoding technique for sensor signals; and (iii) the creation of a custom tiny Convolutional Neural Network (CNN) optimized for future near-sensor hardware deployment. The CNN was trained and tested on a literature dataset (w-HAR) and a custom dataset (ST-HAR), both based on a single stretchable sensor. ST-HAR was specifically developed to address the lack of sports-related data from this type of sensor and includes activities performed at speeds from 0.5 to $14 \mathrm{~km} / \mathrm{h}$. Future work will expand this dataset and deploy a custom hardware accelerator for the proposed CNN model.

The present contribution focuses on applying Denoising Diffusion Probabilistic Models to Remote Sensing image classification, generation and super-resolution. Diffusion models are enhanced, including an attention block embedded in a UNet architecture is used to generate images to complement the EuroSAT data set. Furthermore, models with the same architecture super-resolve sentinel-2 optical images. The results indicate that diffusion models with attention can provide a promising methodological path for applications such as estimating the NDVI images most probably associated with given electro-optical and SAR acquisitions thereby overcoming limitations in observability due to cloud cover or solar illumination.

This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, where we analyse the unity proper to organisms by looking at it from different viewpoints. We discuss the theoretical roles of biological time, complexity, theoretical symmetries, singularities and critical transitions. We explicitly borrow from the conclusions in some key chapters and introduce them by a reflection on "incompleteness", also proposed in the book. We consider that incompleteness is a fundamental notion to understand the way in which we construct knowledge. Then we will introduce an approach to biological dynamics where randomness is central to the theoretical determination: randomness does not oppose biological stability but contributes to it by variability, adaptation, and diversity. Then, evolutionary and ontogenetic trajectories are continual changes of coherence structures involving symmetry changes within an ever-changing global stability.

Effective data visualization is a key part of the discovery process in the era of “big data”. It is the bridge between the quantitative content of the data and human intuition, and thus an essential component of the scientific path from data into knowledge and understanding. Visualization is also essential in the data mining process, directing the choice of the applicable algorithms, and in helping to identify and remove bad data from the analysis. However, a high complexity or a high dimensionality of modern data sets represents a critical obstacle. How do we visualize interesting structures and patterns that may exist in hyper-dimensional data spaces? A better understanding of how we can perceive and interact with multidimensional information poses some deep questions in the field of cognition technology and human-computer interaction. To this effect, we are exploring the use of immersive virtual reality platforms for scientific data visualization, both as software and inexpensive commodity hardware. These potentially powerful and innovative tools for multi-dimensional data visualization can also provide an easy and natural path to a collaborative data visualization and exploration, where scientists can interact with their data and their colleagues in the same visual space. Immersion provides benefits beyond the traditional “desktop” visualization tools: it leads to a demonstrably better perception of a datascape geometry, more intuitive data understanding, and a better retention of the perceived relationships in the data.

Under a variety of names, and in a more or less explicit form, the concept that we now call ‘probability’ must have taken shape in the mind of human beings since the dawn of thought, as a nuance added to the idea of chance (randomness) or unpredictability, though chance may not be exactly the right word. Some time later, the concepts of what we now describe as ‘statistics’ and ‘statistically stable’, moved away from the idea of ‘chance’ and came closer to something else, which was called ‘probability’ and has been fuzzily conceived as being, in some sense, abstract and ‘ideal’. Throughout history it has been felt that unpredictability can have degrees, and that it can be measured using probabilities.

The main promotor of this special issue, Mioara Mugur-Schächter, organised a final debate for the one day conference dedicated to the theme of this special issue of Mathematical Structures in Computer Science.

The amount of collected data in many scientific fields is increasing, all of them requiring a common task: extract knowledge from massive, multi parametric data sets, as rapidly and efficiently possible. This is especially true in astronomy where synoptic sky surveys are enabling new research frontiers in the time domain astronomy and posing several new object classification challenges in multi dimensional spaces; given the high number of parameters available for each object, feature selection is quickly becoming a crucial task in analyzing astronomical data sets. Using data sets extracted from the ongoing Catalina Real-Time Transient Surveys (CRTS) and the Kepler Mission we illustrate a variety of feature selection strategies used to identify the subsets that give the most information and the results achieved applying these techniques to three major astronomical problems.

Computability has its origins in Logic within the framework formed along the original path laid down by the founding fathers of the modern foundational analysis for Mathematics (Frege and Hilbert). This theoretical itinerary, which was largely focused on Logic and Arithmetic, departed in principle from the renewed relations between Geometry and Physics occurring at the time. In particular, the key issue of physical measurement, as our only access to ‘reality’, played no part in its theoretical framework. This is in stark contrast to the position in Physics, where the role of measurement has been a core theoretical and epistemological issue since Poincaré, Planck and Einstein. Furthermore, measurement is intimately related to unpredictability, (in-)determinism and the relationship with physical space–time. Computability, despite having exact access to its own discrete data type, provides a unique tool for the investigation of ‘unpredictability’ in both Physics and Biology through its fine-grained analysis of undecidability – note that unpredictability coincides with physical randomness in both classical and quantum frames. Moreover, it now turns out that an understanding of randomness in Physics and Biology is a key component of the intelligibility of Nature. In this paper, we will discuss a few results following along this line of thought.

This paper provides a conceptual analysis of the role of the mathematical continuumversusthe discrete in the understanding of randomness as a notion with a physical meaning or origin. The presentation is ‘informal’ as we will not write formulas; however, we will refer to non-obvious technical results from various scientific domains, and we will also propose a conceptual framework for understanding randomness (and predictability), which we believe is, essentially, original. As a matter of fact, unpredictability and randomness may be conveniently identified in various physico-mathematical contexts. This will allow us to explore these concepts in continuousversusdiscrete frameworks, with particular emphasis on the relationships and differences between classical approaches and quantum theories in Physics.

MOTIVATION: The huge growth in gene expression data calls for the implementation of automatic tools for data processing and interpretation. RESULTS: We present a new and comprehensive machine learning data mining framework consisting in a non-linear PCA neural network for feature extraction, and probabilistic principal surfaces combined with an agglomerative approach based on Negentropy aimed at clustering gene microarray data. The method, which provides a user-friendly visualization interface, can work on noisy data with missing points and represents an automatic procedure to get, with no a priori assumptions, the number of clusters present in the data. Cell-cycle dataset and a detailed analysis confirm the biological nature of the most significant clusters. AVAILABILITY: The software described here is a subpackage part of the ASTRONEURAL package and is available upon request from the corresponding author. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bioinformatics systems benefit from the use of data mining strategies to locate interesting and pertinent relationships within massive information. For example, data mining methods can ascertain and summarize the set of genes responding to a certain level of stress in an organism. Even a cursory glance through the literature in journals, reveals the persistent role of data mining in experimental biology. Integrating data mining within the context of experimental investigations is central to bioinformatics software. In this paper we describe the framework of probabilistic principal surfaces, a latent variable model which offers a large variety of appealing visualization capabilities and which can be successfully integrated in the context of microarray analysis. A preprocessing phase consisting of a nonlinear PCA neural network which seems to be very useful to deal with noisy and time dependent nature of microarray data has been added to this framework.

The recent technological advances are producing huge data sets in almost all fields of scientific research, from astronomy to genetics. Although each research field often requires ad-hoc, fine tuned, procedures to properly exploit all the available information inherently present in the data, there is an urgent need for a new generation of general computational theories and tools capable to boost most human activities of data analysis. Here, we propose probabilistic principal surfaces (PPS) as an effective high-D data visualization and clustering tool for data mining applications, emphasizing its flexibility and generality of use in data-rich field. In order to better illustrate the potentialities of the method, we also provide a real world case-study by discussing the use of PPS for the analysis of yeast gene expression levels from microarray chips.

This provocative synthetic introduction to several research themes aims at stimulating a reflection on our mature science, Informatics, beyond the myths that originated it and that, today, may affect its progress. The awareness of the expressiveness and of the internal limitations of digital computing is a necessary step, within the Computer Science community, to improve the relations to other sciences, where computers are increasingly used as tools. We will briefly hint to simulations problems in Physics and discuss the still prevailing projection of our fantastic machine onto Biological and Cognitive phenomena. The conference lecture will mostly focus on §.3.

Computer Science has witnessed the emergence of a plethora of different logics, models and paradigms for the description of computation. Yet, the classic Church–Turing thesis may be seen as indicating that all general models of computation are equivalent. Alan Perlis referred to this as the ‘Turing tarpit’, and argued that some of the most crucial distinctions in computing methodology, such as sequential versus parallel, deterministic versus non-deterministic, local versus distributed disappear if all one sees in computation is pure symbol pushing. How can we express formally the difference between these models of computation?

The relation of inclusion between types has been suggested by the practice of programming as it enriches the polymorphism of functional languages. We propose a simple (and linear) sequent calculus for subtyping as logical entailment. This allows us to derive a complete and coherent approach to subtyping from a few, logically meaningful sequents. In particular, transitivity and anti-symmetry will be derived from elementary logical principles.

One of the most relevant problems in the extraction of scientifically useful information from wide field astronomical images (both photographic plates and CCD frames) is the recognition of the objects against a noisy background and their classification in unresolved (starlike) and resolved (galaxies) sources. In this paper we present a neural network based method capable to perform both tasks and discuss in detail the performance of object detection in a representative celestial field. The performance of our method is compared to that of other methodologies often used within the astronomical community.

The relation of inclusion between types has been suggested by the practice of programming, as it enriches the polymorphism of functional languages. We propose a simple (and linear) calculus of sequents for subtyping as logical entailment. This allows to derive a complete and coherent approach to subtyping from a few, logically meaningful, sequents. In particular, transitivity and anti-symmetry are derived from elementary logical principles, which stresses the power of sequents and Gentzen-style proof methods. Indeed, proof techniques based on cut-elimination are at the core of our results.

The authors focus on how polymorphic functions, which may take types as inputs, depend on types. These functions are generally understood to have an essentially constant meaning, in all models, on input types. It is shown how the proof theory of the polymorphic lambda -calculus suggests a clear syntactic description of this phenomenon. Under a reasonable condition, it is shown that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).>

A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. Using the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. Using the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having “invertible” proofs between the two terms. Work of Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.

Abstract Quest is a programming language based on impredicative type quantifiers and subtyping within a three-level structure of kinds, types and type operators, and values. The semantics of Quest is rather challenging. In particular, difficulties arise when we try to model simultaneously features such as contravariant function spaces, record types, subtyping, recursive types and fixpoints. In this paper we describe in detail the type inference rules for Quest, and give them meaning using a partial equivalence relation model of types. Subtyping is interpreted as in previous work by Bruce and Longo (1989), but the interpretation of some aspects – namely subsumption, power kinds, and record subtyping – is novel. The latter is based on a new encoding of record types. We concentrate on modelling quantifiers and subtyping; recursion is the subject of current work.

Various Theories of Types are introduced, by stressing the analogy ‘propositions-as-types’: from propositional to higher order types (and Logic). In accordance with this, proofs are described as terms of various calculi, in particular of polymorphic (second order) λ-calculus. A semantic explanation is then given by interpreting individual types and the collection of all types in two simple categories built out of the natural numbers (the modest sets and the universe of ω-sets). The first part of this paper (syntax) may be viewed as a short tutorial with a constructive understanding of the deduction theorem and some work on the expressive power of first and second order quantification. Also in the second part (semantics, §§6–7) the presentation is meant to be elementary, even though we introduce some new facts on types as quotient sets in order to interpret ‘explicit polymorphism’. (The experienced reader in Type Theory may directly go, at first reading, to §§6–8).

The authors give a formal semantics for the language Bounded Fun, which supports both parametric and subtype polymorphism. They show how to use partial equivalence relations to model inheritance in this language, which supports the notion of subtype and record types. A generalization of partial equivalence relations, known as omega -sets, is used in combination with modest sets to provide the first known model of Bounded Fun (with explicit polymorphism). Connections with previous work on the semantics of explicit parametric polymorphism is established by noting that the semantics of polymorphic types presented here (using dependent products) is isomorphic to that given by the intersection interpretation of polymorphism.>

Article Free Access Share on Provable isomorphisms and domain equations in models of typed languages Authors: K B Bruce Department of Mathematical Sciences, Williams College, Williamstown, Ma. Department of Mathematical Sciences, Williams College, Williamstown, Ma.View Profile , G Longo Dipartimento di Informatica, Universita di Pisa, Pisa, Italy Dipartimento di Informatica, Universita di Pisa, Pisa, ItalyView Profile Authors Info & Claims STOC '85: Proceedings of the seventeenth annual ACM symposium on Theory of computingDecember 1985 Pages 263–272https://doi.org/10.1145/22145.22175Published:01 December 1985Publication History 31citation248DownloadsMetricsTotal Citations31Total Downloads248Last 12 Months21Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Abstract A type-structure of partial effective functionals over the natural numbers, based on a canonical enumeration of the partial recursive functions, is developed. These partial functionals, defined by a direct elementary technique, turn out to be the computable elements of the hereditary continuous partial objects; moreover, there is a commutative system of enumerations of any given type by any type below (relative numberings). By this and by results in [1] and [2], the Kleene-Kreisel countable functionals and the hereditary effective operations (HEO) are easily characterized.

A classification of all probability distributions over the finite alphabet of an information source is given, where the classes are the sets of distributions sharing the same binary Huffman code. Such a classification can be used in noiseless coding, when the distribution of the finite memoryless source varies in time or becomes gradually known. Instead of applying the Huffman algorithm to each new estimate of the probability distribution, if a simple test based on the above classification is passed, then the Huffman code used previously is optimal also for the new distribution.

A new approach to the classical fixed-length noiseless source coding problem is proposed for the case of finite ergodic Markov sources. This approach is based on simple counting arguments. The central notion of "Markov type" (a set containing all the source sequences having the same transition counts from letter to letter) is introduced and the cardinality of such a set is evaluated via graph theoretical tools. The error exponent is shown to be a weighted average of informational divergences, and the universal character of the result is stressed. As a corollary, the classical source coding theorem (determining the achievable rates) is rederived.

A combinatorial approach is proposed for proving the classical source coding theorems for a finite memoryless stationary source (giving achievable rates and the error probability exponent). This approach provides a sound heuristic justification for the widespread appearence of entropy and divergence (Kullback's discrimination) in source coding. The results are based on the notion of composition class -- a set made up of all the distinct source sequences of a given length which are permutations of one another. The asymptotic growth rate of any composition class is precisely an entropy. For a finite memoryless constant source all members of a composition class have equal probability; the probability of any given class therefore is equal to the number of sequences in the class times the probability of an individual sequence in the class. The number of different composition classes is algebraic in block length, whereas the probability of a composition class is exponential, and the probability exponent is a divergence. Thus if a codeword is assigned to all sequences whose composition classes have rate less than some rateR, the probability of error is asymptotically the probability of the must probable composition class of rate greater thanR. This is expressed in terms of a divergence. No use is made either of the law of large numbers or of Chebyshev's inequality.

Any finite information source is given a graph structure, in which two vertices are adjacent whenever the two corresponding source letters are distinguishable by the coder-decoder pair. Usual sources correspond, therefore, to complete graphs. If the associated graph is not complete, however, an\varepsilon-code for the source can be constructed in two steps: in the first, distinct codewords are given to distinguishable letters only; in the second step, a similar encoding is carried out for the complementary graph, in which distinguishable letters become indistinguishable and the converse. A particularly simple case shows up when nonadjacency is an equivalence relation among the vertices of the graph: each class of nondistinguishable letters can then be considered as a letter in a coarser source alphabet. The two-step procedure is then particularly intuitive. A problem arises when this procedure does not destroy optimality of the resulting\varepsilon-code; some partial results are given in this direction. The results obtained are largely based on some graph-theoretical ideas and tools.