Although the cortico-basal ganglia-thalamic (CBGT) network is identified as a central circuit for decision-making, the dynamic interplay of multiple control pathways within this network in shaping decision trajectories remains poorly understood. Here we develop and apply a novel computational framework-CLAW (Circuit Logic Assessed via Walks)-for tracing the instantaneous flow of neural activity as it progresses through CBGT networks engaged in a virtual decision-making task. Our CLAW analysis reveals that the complex dynamics of network activity is functionally dissectible into two critical phases: deliberation and commitment. These two phases are governed by distinct contributions of underlying CBGT pathways, with indirect and pallidostriatal pathways influencing deliberation, while the direct pathway drives action commitment. We translate CBGT dynamics into the evolution of decision-related policies, based on three previously identified control ensembles (responsiveness, pliancy, and choice) that encapsulate the relationship between CBGT activity and the evidence accumulation process. Our results demonstrate two contrasting strategies for decision-making. Fast decisions, with direct pathway dominance, feature an early response in both boundary height and drift rate, leading to a rapid collapse of decision boundaries and a clear directional bias. In contrast, slow decisions, driven by indirect and pallidostriatal pathway dominance, involve delayed changes in both decision policy parameters, allowing for an extended period of deliberation before commitment to an action. These analyses provide important insights into how the CBGT circuitry can be tuned to adopt various decision strategies and how the decision-making process unfolds within each regime.
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of interpolation--namely, Craig interpolation and deductive interpolation. Our discussion focuses primarily on how these properties present in families of logical systems taken as a whole, particularly those comprising all axiomatic extensions of any of several notable non-classical logics. We consider a range of important examples: superintuitionistic and modal logics, fuzzy logics, paraconsistent logics, relevant logics, and substructural logics.
We introduce an intuitionistic modal logic strictly contained in the intuitionistic modal logic IK and being an appropriate candidate for the title of ``minimal normal intuitionistic modal logic''.
Rita Andreoni-Pham, Hereroa Johnston, Jacob F. Warner
et al.
Abstract A long-held hypothesis in regeneration proposes that developmental processes are re-deployed during regeneration. To investigate this, we compared embryonic and regeneration gene regulatory networks (GRN) in the sea anemone Nematostella vectensis using transcriptomic time series spanning these two developmental trajectories. Here, we show that regeneration reuses cohorts of the embryonic genes along with a small set of genes whose expression dynamics are specific to regeneration. We identified co-expression modules that are either conserved between embryogenesis and regeneration or specific to regeneration, with the latter linked to cellular mechanisms such as apoptosis, tissue remodeling, and wound healing. Functional assays revealed that apoptosis and cWnt signaling pathways are partially MEK/ERK dependent, have largely distinct downstream targets but converge to coordinate regenerative responses. Collectively, these results indicate that regeneration in N. vectensis represents a partial redeployment and extensive rewiring of the embryonic GRN, reactivating developmental modules through a regeneration-specific network logic.
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability logic the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical result of the article is a proof of the soundness and completeness of CL18 with respect to the semantics of computability logic.
DNA computing has gained widespread attention for leveraging the unique properties of DNA molecules to perform computational operations. As a fundamental tool for analyzing data and optimizing models, matrix operation plays an important role in intensive computational tasks and is a focus of DNA-based numerical computation. However, complex computing tasks are often achieved through transmitting and processing signals successively, which requires matrix operation to perform calculations sequentially. Therefore, it is important to find a way to perform successive matrix operation to ensure computational sustainability in molecular computing. In this paper, we present a successive DNA matrix operation method based on the mechanism of combinatorial allosteric DNA strand displacement. In this mechanism, the input signal and the output signal are completely decoupled in the base arrangement of the DNA domain, which makes it easy to implement successive DNA matrix operation and easily realize the connection of DNA signal processing units. Based on this mechanism, some basic DNA logic gates, such as AND gate, OR gate, and INHIBIT gate, were constructed first, then Boolean matrix multiplication was realized and, finally, matrix-chain multiplication was completed to illustrate successive DNA matrix operation. This study provides a new way to implement successive DNA matrix operation and enriches the toolbox for achieving intensive computational tasks through molecular computing.
This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental model-theoretic notion of type.
Fuzzy logic is a way to argue with boolean predicates for which we only have a confidence value between 0 and 1 rather than a well defined truth value. It is tempting to interpret such a confidence as a probability. We use Markov kernels, parametrised probability distributions, to do just that. As a consequence we get general fuzzy logic connectives from probabilistic computations on products of the booleans, stressing the importance of joint confidence functions. We discuss binary logic connectives in detail and recover the "classic" fuzzy connectives as bounds for the confidence for general connectives. We push multivariable logic formulas as far as being able to define fuzzy quantifiers and estimate the confidence.
Molecular circuits and devices with temporal signal processing capability are of great significance for the analysis of complex biological processes. Mapping temporal inputs to binary messages is a process of history-dependent signal responses, which can help understand the signal-processing behavior of organisms. Here, we propose a DNA temporal logic circuit based on DNA strand displacement reactions, which can map temporally ordered inputs to corresponding binary message outputs. The presence or absence of the output signal is determined by the type of substrate reaction with the input so that different orders of inputs correspond to different binary outputs. We demonstrate that a circuit can be generalized to more complex temporal logic circuits by increasing or decreasing the number of substrates or inputs. We also show that our circuit had excellent responsiveness to temporally ordered inputs, flexibility, and expansibility in the case of symmetrically encrypted communications. We envision that our scheme can provide some new ideas for future molecular encryption, information processing, and neural networks.
An involutive Stone algebra (IS-algebra) is a structure that is simultaneously a De Morgan algebra and a Stone algebra (i.e. a pseudo-complemented distributive lattice satisfying the well-known Stone identity ~xv~~x=1). IS-algebras have been studied algebraically and topologically since the 1980's, but a corresponding logic (here denoted IS$\leq$) has been introduced only very recently. The logic IS$\leq$ is the departing point for the present study, which we then extend to a wide family of previously unknown logics defined from IS-algebras. We show that IS$\leq$ is a conservative expansion of the Belnap-Dunn four-valued logic (i.e. the order-preserving logic of the variety of De Morgan algebras), and we give a finite Hilbert-style axiomatization for it. More generally, we introduce a method for expanding conservatively every super-Belnap logic so as to obtain an extension of IS$\leq$. We show that every logic thus defined can be axiomatized by adding a fixed finite set of rule schemata to the corresponding super-Belnap base logic. We also consider a few sample extensions of IS$\leq$ that cannot be obtained in the above-described way, but can nevertheless be axiomatized finitely by other methods. Most of our axiomatization results are obtained in two steps: through a multiple-conclusion calculus first, which we then reduce to a traditional one. The multiple-conclusion axiomatizations introduced in this process, being analytic, are of independent interest from a proof-theoretic standpoint. Our results entail that the lattice of super-Belnap logics (which is known to be uncountable) embeds into the lattice of extensions of IS$\leq$. Indeed, as in the super-Belnap case, we establish that the finitary extensions of IS$\leq$ are already uncountably many.
In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over $\mathbb{Z}_{2^i}$ cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism problem. We thereby separate rank logic from CPT and in particular from polynomial time.
Nishanth Nakshatri, Arjun Menon, C. Lee Giles
et al.
We present a synthetic prediction market whose agent purchase logic is defined using a sigmoid transformation of a convex semi-algebraic set defined in feature space. Asset prices are determined by a logarithmic scoring market rule. Time varying asset prices affect the structure of the semi-algebraic sets leading to time-varying agent purchase rules. We show that under certain assumptions on the underlying geometry, the resulting synthetic prediction market can be used to arbitrarily closely approximate a binary function defined on a set of input data. We also provide sufficient conditions for market convergence and show that under certain instances markets can exhibit limit cycles in asset spot price. We provide an evolutionary algorithm for training agent parameters to allow a market to model the distribution of a given data set and illustrate the market approximation using three open source data sets. Results are compared to standard machine learning methods.
Abstract Dual-chamber pacemaker is a fully automatic pacemaker with the function of simulating human physiological pacing. It regulates pacing by programming different refractory periods and various special functions, which are closely related to arrhythmia. After in-depth understanding of these special functions, regular electrocardiogram follow-up analysis is required to provide individualized optimal program control and so is appropriate the administration of the pacemaker’s special functions to better provide optimal clinical guidance for patients with arrhythmia.
Surgery, Diseases of the circulatory (Cardiovascular) system
Heba Saadeh, Maha Saadeh, Wesam Almobaideen
et al.
COVID-19 is a global pandemic that affected the everyday life activities of billions around the world. It is an unprecedented crisis that the modern world had never experienced before. It mainly affected the economic state and the health care system. The rapid and increasing number of infected patients overwhelmed the healthcare infrastructure, which causes high demand and, thus, shortage in the required staff members and medical resources. This shortage necessitates practical and ethical suggestions to guide clinicians and medical centers when allocating and reallocating scarce resources for and between COVID-19 patients. Many studies proposed a set of ethical principles that should be applied and implemented to address this problem. In this study, five different ethical principles based on the most commonly recommended principles and aligned with WHO guidelines and state-of-the-art practices proposed in the literature were identified, and recommendations for their applications were discussed. Furthermore, a recent study highlighted physicians' propensity to apply a combination of more than one ethical principle while prioritizing the medical resource allocation. Based on that, an ethical framework that is based on Fuzzy inference systems was proposed. The proposed framework's input is the identified ethical principles, and the output is a weighted value (per patient). This value can be used as a rank or a priority factor given to the patients based on their condition and other relevant information, like the severity of their disease status. The main idea of implementing fuzzy logic in the framework is to combine more than one principle when calculating the weighted value, hence mimicking what some physicians apply in practice. Moreover, the framework's rules are aligned with the identified ethical principles. This framework can help clinicians and guide them while making critical decisions to allocate/reallocate the limited medical resources during the current COVID-19 crisis and future similar pandemics.
In the framework of propositional Łukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic in theories in Łukasiewicz logic is obtained. Some of these results were already presented in Hájek's "Metamathematics of Fuzzy Logic" as technical statements. A connection to the lack of (deductive) Beth property in Łukasiewicz logic is drawn. Moreover, while irrational elements of the standard semantics are not implicitly definable by finitary means, a parallel development is possible for them in the infinitary Łukasiewicz logic. As an application of definability of the rationals, it is shown how computational complexity results for Rational Pavelka logic can be obtained from analogous results for Łukasiewicz logic. The complexity of the definability notion itself is studied as well. Finally, we review the import of these results for the precision/vagueness discussion for fuzzy logic, and for the general standing of truth constants in Łukasiewicz logic.
The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so far this has been proved by cut-elimination for ad-hoc sequent calculi. Here we use the methods of natural deduction and Curry-Howard correspondence to provide a simple computational interpretation of the logic.