Abstract: The rapid advancement of biomedical technologies has necessitated the development of energy-efficient signal processing circuits, particularly in portable and wearable medical devices. This paper explores the design and implementation of such circuits, focusing on the processing of critical biomedical signals, including electrocardiograms (ECG), electroencephalograms (EEG), and electromyograms (EMG). As healthcare increasingly shifts towards remote monitoring and personalized medicine, the need for low-power solutions that maintain high performance becomes paramount. This study begins by outlining the fundamental characteristics of various biomedical signals and the inherent challenges faced in signal processing, particularly concerning power consumption and signal integrity. We delve into innovative circuit design techniques, emphasizing low-power analog circuit architectures, digital signal processing (DSP) methodologies, and effective power management strategies. Key approaches such as dynamic voltage and frequency scaling (DVFS), algorithm optimization, and hardware-software co-design are discussed, highlighting their roles in enhancing energy efficiency without compromising performance. The paper presents several case studies that illustrate the practical application of these design principles, including a prototype ECG signal processing circuit and an EEG acquisition system. Performance metrics such as power consumption and signal-to-noise ratios (SNR) are analyzed, demonstrating significant improvements over traditional designs. The findings emphasize the potential for energy-efficient circuits to impact the overall performance and usability of biomedical devices. In addition, the paper identifies limitations and challenges encountered during the design and implementation phases, offering insights into areas for future research. Emerging technologies, including the integration of artificial intelligence and machine learning, are considered as avenues for further enhancing energy efficiency in biomedical signal processing. Ultimately, this study underscores the critical importance of developing energy-efficient circuits in advancing modern healthcare solutions and improving patient outcomes through effective monitoring and diagnosis.

Abstract: José Morgado introduced in 1962 an original and interesting notion of hyperlattices, that he called reticuloides. In his Master’s thesis defended in 1971 (and supervised by Newton da Costa), Antonio M. Sette proposed a novel notion of implicative hyperlattices (here called SIHLs) based on Morgado’s hyperlattices. He also extended SIHLs by adding an unary hyperoperator, obtaining a class of hyperalgebras (here called SHCωs) which correspond to da Costa algebras for Cω, being so a suitable semantics for the logic Cω. In this paper, after characterizing Sette’s implicative hyperlattices in (hyper)lattice-theoretic terms, and proving some basic results on SIHLs, we introduce a class of swap structures, a special class of hyperalgebras over the signature of Cω naturally induced by implicative lattices. It is proven that these swap structures are indeed SHCωs. Finally, it is proven that the class of SHCωs, as well as the above mentioned class of swap structures, characterize the logic Cω.

Abstract: We propose a novel methodology to encode legislation in a formal language (specifically Defeasible Deontic Logic). After the presentation of the methodology, we report on the results of an empirical evaluation and compare them with the outcome of a previous experiment. The comparison suggests a significant improvement over the previous experiment.

Abstract: Over the last 25 years, flood research has experienced a significant transition. Researchers and authorities used to study flood control but nowadays they focus on flood resilience. The underlying reason is a global increase in the frequency and intensity of flood events and the subsequent need for proactive resilience building instead of reactive disaster response. This shift led both the scientific community and society to look for more dynamic and adaptive approaches to environmental risk assessments, in an attempt to understand and quantify vulnerabilities. This article studies a novel computational approach to flood resilience, integrating rule-based agent modeling with mathematical dynamic analysis. This approach, called BRIDGES, presents a rule-based agent system that intends to simulate water propagation along with key factors influencing flood resilience. To this end, it attempts to analyze flood events, their emergent behavior as well as the usual environmental responses. As a result, a promising flood risk assessment and environmental management approach based on the combination of agent-based systems and dynamical rule-based systems is revealed in this study. After all, civil protection authorities and researchers agree that the aim now is to learn how to live with floods.

Abstract: Logics of Statements in Context have been proposed as a general framework to describe and relate, in a uniform and unifying way, a broad spectrum of logics and specification formalisms which also comprise “open formulas”. Especially, it has been shown that we can define arbitrary first-order “open formulas” in arbitrary categories. At present, there are two deficiencies. In the general case only signatures with predicate symbols are considered and institutions of statements in context are only defined for single signatures. In this paper we elaborate the special case of traditional many-sorted First-Order Logic. We show that any many-sorted first-order signature Σ with predicate and (!) operation symbols gives rise to an institution FLΣ of Σ-statements in context, and that any signature morphism results in a comorphism between the corresponding institutions. We prove that we obtain a functor FL:Sig→coIns from the category of signatures into the category of institutions and comorphisms. We construct a corresponding Grothendieck institution FL♯ and prove that FL♯ is indeed an extension of the traditional institution of First-Order Logic which only comprises “closed formulas”. We also investigate substitutions in detail and discuss (elementary) diagrams in the sense of traditional First-Order Logic.

Abstract: This paper provides a set of category-theoretic analyses of Gödel’s incompleteness theorems and Tarski’s indefinability theorem (see Appendix). We view the first-order theory as a mathematical language and introduce the notion of "language charge" as a monad within a category. For each analysis, we introduce a pair of adjunct categories: a syntactic category and a semantic category. We show that the Gödel numbering can be modeled as a pair of adjoint functors between these categories—a right functor from syntax to semantics and a left functor in the reverse direction. We prove that the Gödel numbering functor serves as a limit in a functor category. Additional analyses focus on the expressibility and definability in the twin theorems. Each of these is linked to natural transformations. In addition, we establish a formal account of "spontaneous naturality breaking" in the context of Gödel’s independent statements and Tarski’s indefinability. Finally, it touches higher order categories. By composing a syntactic category and a semantic category, we constructed a 2-Category with two layers of structures. Note that 2-category is one of the current research interests in category theory. Further, by decomposing and recomposing the syntactic category, we constructed a 3-Category.

Abstract: The set of Boolean functions has a simple basis formed by the meet and the negation. Is it possible to have a similarly basis for any subset of finitary operations on a finite set with more than three elements? It is known that any set of finitary operations on a finite set can be expressed as a set of operations preserving some relations on this set. A clone on a finite set is a set of finitary operations on this set containing all the projections and stable by composition. It is also known that the set of clones on a finite set is a complete lattice. The maximal elements of this lattice was completely described by Rosenberg in 1965. In this paper, we determine clones of the form $\Pol \sigma \cap \Pol \lambda$ sited directly below $\Pol \lambda$ where $\lambda$ is a fixed regular relation and $\sigma$ a binary relation to be characterized.

Abstract: The following two consequences of the axiom of constructibility V = L are established for every n ≥ 3: 1. Every linear $\bf\Sigma^1_n$ set is the projection of a uniform planar $\bf\Pi^1_{n-1}$ set. 2. There is a planar $\bf\Pi^1_{n-1}$ set with countable cross-sections, not covered by a union of countably many uniform $\bf\Sigma^1_n$ sets. If n = 2 then claims 1,2 hold in ZFC alone, without the assumption of V = L.

Abstract: Probability is initially defined on a Boolean algebra or a lattice of projectors. We propose here to start from a Heyting algebra.

Abstract: Knowledge is not merely the characteristic of certain pieces of information being deemed true, believed and justifiable, but rather a process. The sentences that reaches the status of knowledge forms a universe that provides an interpretation of the reality one aims to describe. Language exchanges information through communication and the justification, if concludes successfully with respect to a sentence, it elevates the information to the status of knowledge. We provide a model where we define the fundamental elements of communication and grammar. As a result, knowledge must be \open\ (everyone must be able to acquire it), \free\ (everyone must be able to justifiy) and \tidy\ (everyone must be able to retrace the justification process in all its parts recursively). Ultimately, the development of knowledge processing, referred to as \emph{knowmatic}, represents the evolution of the information technologies (\it).

Abstract: Imbalanced classes can cause machine learning models to classify positive class instances poorly, and the models require hyperparameter sets to optimal values. This study aims to develop random forest (RF) and support vector machine (SVM) models that use the optimal hyperparameters obtained through 5-fold cross-validation data. Both models were trained using optimal hyperparameter pairs that fit two data scenarios, the original and oversampling training sets, to produce the benchmark and best models. The model's performance was evaluated using six metrics, including training and testing data. The acquired optimal RF hyperparameter pair was (500, 10) for the minimum number of instances and tree depth level. In contrast, the acquired optimal SVM hyperparameter pair was (0.001, 500) for the gamma and constant values. The benchmark model performed approximately 98% on Accuracy, Precision, Recall, and F1 score metrics but failed to deliver any performance on Mathew's Correlation Coefficient (MC) and Area under Curve (AUC) metrics. The best RF and SVM perform less than both benchmark models in four famous metrics. Both best models have performance improvements of approximately 6% and 11% for the MCC and AUC metrics, respectively. The best RF performance was slightly better than the best SVM performance.

Abstract: This article describes an approach for optimising sensor-controlled systems through minimal intervention, utilising Fuzzy Linear Systems of Equations (FLSE). Staring with a generalised model of the system behaviour, incorporating an array of control units, environmental sensors, and an expert knowledge base. The described problems of detecting the level of intervention needed to change the system state to another is handled with the help of developed methods for solving the inverse problem for FLSE. By achieving minimal intervention, we ensure that system adjustments effective, economically optimal and non-intrusive. A MATLAB-based implementation is presented.

Abstract: This paper considers a specific fragment of Linear Temporal Logic for Finite traces, DECLAREd, which, to the best of our knowledge, we prove for the first time to be a {polytime} fragment of LTLf. We derive this in terms of the following ancillary results: we propose a set of novel LTLf equivalence rules that, when applied to \LTLf specifications, lead to an equivalent specification which can be computed faster by any existing verified temporal artificial intelligence task. We also introduce the concept of temporal non-simultaneity, prescribing that two activities shall never satisfy the same atom, and temporal short-circuit, that occurs when a specification interpreted in LTL would accept an infinitely long trace while, on LTLf, it can be rewritten so to postulate the absence of certain activity labels. We test these considerations over formal synthesis (Lydia), SAT-Solvers (AALTAF) and formal verification (KnoBAB) tools, where formal verification can be also run on top of a relational database and can be therefore expressed in terms of relational query answering. We show that all these benefit from the aforementioned assumptions, as running their tasks over a rewritten equivalent specification will improve their running times.

Abstract: We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any formal theorem of any mathematician from past or present forever belongs to K. We assume that mathematical sets are atemporal entities. In this article, they exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X ⊆ N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X.

Abstract: The classical propositional calculus (zero-order logic, classical propositional logic), is the most fundamental two-valued logical system. In this paper we present a proof of inconsistency of the classical propositional calculus. Then, we get right away the conclusion that the metatheory of the classical propositional calculus is inconsistent.

Abstract: The implementation of Boolean functions using Nano crossbar- based switching lattices has been suggested as a substitute for conventional CMOS-based approaches in digital circuits . This alternative may satisfy the needs of future electronic designs, con- sidering the expected end of Moore’s law. This study introduces CVM, a Crossbar-based circuit Verification through Modeling tech- nique

Abstract: Our natural language approach concerns syntactic analysis using a dedicated Javascript library - wink-nlp - and semantic analysis based on Prolog programming language, facilitated by another Javascript library - tau-prolog - that allows defining logical programs, declaring rules and checking for goals inside Javascript language. Firstly, our program splits the original text into sentences, than into tokens and identifies each part of the sentence, dynamically maps entities into Prolog rules, then check the spelling accordingly to the Definite Clause Grammar (DCG) by querying the pre-defined program for initial goals (the sentence itself). Basically, we let the parser infer its own rules from the syntactic point of view, then check the grammar from a semantic perspective against the DCG inside the same work flow or pipeline of steps.The provided article combine the usage of wink-nlp and tau-prolog packages for natural language processing (NLP) and understanding (NLU), demonstrates the need of a supplementary logic layer based on beta reductions and provide a method to convert lambda abstractions into arrow Javascript functions.

Abstract: Investment management is a common process and practice used for achieving a desirable investment goal or outcome. Investment assessment should be carried out at various stages of project realization in accordance with capital investment volume. Investment risk management implies the effective control of all procedures and monitoring of risks in all phases of the investment project. Because of the reason that a single indicator in probability calculation of achieving optimal return from the investment does not exist, performing sufficiently reliable estimates of the quality of investments becomes a tedious task. There are many indicators, factors, and criteria required for consideration to reach the effective solution of the investment problem. Unfortunately, the systematic variation of economic situations in the marketplace stipulates the continuous and frequent changes of investment conditions and environment in which the investor should act and operate. Hence, the rules required for providing a reasonable quality of investment projects can be based only on investor’s management strategy and rely on investor’s intuition and practice. The importance of classification in investment management and decision making process is undeniable. The objects to be classified are described using assessments in accordance with various criteria which can be both quantitative and qualitative. With a competent formulation of the investment process, both methods are used in parallel. There exist various decision making approaches for the investment management, and simple additive weighting (SAW) is one of the well-known multi-criteria decision making (MCDM) methods aiming to provide an optimal decision for decision maker when solving various real-life problems, and particularly, investment problem. In this paper, fuzzy simple additive weighting (FSAW) method in group decision making is applied to undertake the capital investment expenditure for purchasing cars with the purpose of renting them to the public. The development of existing FSAW method is accomplished and this process involves the sensibility of outcomes to changes in the rate of fuzziness represented with decisions taken. Eventually, the degree of fuzziness involved in an analysis that directly attempts to model the immanent vagueness and imperfectness in particular precedency judgments made, is determined. A numerical example illustrates the importance and effectiveness of the suggested approach with the aim of ranking alternatives and hence, determining the most preferred alternative in MCDM problem.

Abstract: We revise the definition of graph operations in [WDK2018] and adapt correspondingly the construction of graph term algebras. As a first contribution to a prospective research field Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. Especially, we generalize the concept generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct for any graph operation expression a corresponding derived graph operation in any graph algebra.

Abstract: We find at least 4 quantum properties that are indeed universal in some number systems; and we can use them for quantum consciousness. Using the sets B={0,1}, N, Z, or Q has the +4 quantum properties that one can trust, as archetypes of easy communication to friends and foes, to ignoranti or cognoscenti, and for quantum computing. This paper proposes the use of Bayesian geometry to reduce the space of possible results, reducing or increasing initial beliefs by successive experimentation. This is exemplified in biology and mathematics, and can be applied to physics and other sciences. The conclusion is that an experimental fact can be absolutely verified. Any mathematical choice (as verified by computers) militating against R=Q, is under an absolutely low chance to succeed. Infinitesimals are denied based on 3^16 independent factors. This is not a probabilistic result, but based on reduction of the Bayes geometry for updating beliefs. This work applies to non-probabilistic and unknown phenomena, such as those found in oscillations (neutrino, health), evolution, and quantum computing, denies Gödel's uncertainty, and solves the liar's paradox by reflection. This connects different scientific fields with one another, in an internet, i.e., in a network of connections of multiple open networks, using the set Q, resembling a hologram, and includes entanglement.