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Abstract The human brain’s remarkable efficiency in solving puzzles through pictorial information processing serves as a valuable inspiration for computational puzzle solving. In this study, we present a nucleation algorithm for automated puzzle solving, developed based on statistical analysis of an empirical database. This algorithm effectively solves puzzles by choosing pieces with infrequent and iridescent edges as nucleation centers, followed by the identification of neighboring pieces with high resemblances from the remaining puzzle pieces. For the 8 different pictures examined in this study, both empirical data and computer simulations consistently demonstrate a power-law relationship between solving time and the number of puzzle pieces, with an exponent less than 2. We explain this relationship through the nucleation model and explore how the exponent is influenced by the color pattern of the puzzle picture. Moreover, our investigation of puzzle-solving processes reveals distinct principal pathways, akin to protein folding behavior. Our study contributes to the development of a cognitive model for human puzzle solving and color pattern recognition.

Abstract In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem.

In this study, by using the Meir-Keeler mapping, cyclic Kannan contraction and cyclic Chatterjee contraction, we establish the notions of cyclic Meir-Keeler-Kannan-Chatterjea contraction T : A ∪ B → A ∪ B and cyclic Meir-Keeler-Kannan-Chatterjea contractive pair (T, S) of mappings T : A → B and S : B → A, and then we prove some best proximity point theorems for these various types of cyclic contractions. Our results generalize or improve many recent best proximity point theorems in the literature.

Abstract In this paper, we study the split DC program by using the split proximal linearized algorithm. Further, linear convergence theorem for the proposed algorithm is established under suitable conditions. As applications, we first study the DC program (DCP). Finally, we give numerical results for the proposed convergence results.

Context: Butylidenephthalide (Bdph) has been reported to inhibit rat uterine contractions, but significantly potentiate the noradrenaline (NA)-induced contractions in guinea-pig vas deferens (GPVDs). Objective: The present study elucidates the binding specificity of Bdph in GPVD to potentiate contractions. Materials and methods: Electrical field stimulation (EFS, supramaximal voltage, 1 ms and 1 Hz) or exogenous NA (50 μM) was applied to the GPVD in Krebs or 1/10 Mg-Tyrode’s solution, respectively. After the clonidine (10 nM)-induced twitch inhibition or the exogenous NA-induced contractions reached a constant, Bdph (50 µM) was added 2 min prior to the subsequent addition of NA (50 µM). Three experiments were performed. In the presence of Bdph (100 μM), the release of NA in the medium and remaining NA content in the tissues were determined after EFS-stimulation. Results: Bdph (100 μM) significantly antagonized the clonidine (10 nM)-induced twitch inhibition from 22.5 ± 2.1 to –11.4 ± 1.6% (n = 6) and dibutyryl-cAMP (300 μM) from 25.7 ± 3.2 to 7.9 ± 4.0% (n = 8). Bdph (100 μM) significantly increased the electrically stimulated release of NA from 393.0 ± 109.5 to 1000.0 ± 219.1 ng/g (n = 6). Bdph (50 μM) potentiated the exogenous NA (50 μM)-induced contractions from 3.0 ± 0.06 to 3.9 ± 0.06 g (n = 3), but after washout of Bdph, the response to NA gradually curtailed. Discussion and conclusions: Bdph action may be through the nonspecific binding of the butylidene group to prejunctional α2- and postjunctional α1-adrenoceptors to reversibly block K+ channels, and irreversibly block VDCCs on the smooth muscle cell membrane, respectively.

This paper is aimed at presenting some coincidence point results using admissible mapping in the framework of the partial b-metric spaces. Observed results of the article cover a number of existing works on the topic of “investigation of nonunique fixed points.” We express an example to indicate the validity of the observed outcomes.

In this article, we introduce the notions of a soft inf-comparable contraction and soft comparable Meir-Keeler contraction in a soft metric space. Furthermore, we prove two soft fixed point theorems which assure the existence of soft fixed points for these two types of comparable contractions. The obtained results not only generalize but also unify many recent fixed point results in the literature.

Context: The rhizome of Ligusticum chuaxiong Hort. (Umbelliferae) has been used by Chinese for several thousand years. Its main constituent, butylidenephthalide (Bdph), was proved to be active in inhibiting rat uterine contractions induced by prostaglandin F2α and was reported to be a nonspecific antispamodic and a blocker of voltage-dependent Ca2+ channels (VDCCs). Objectives: The present study investigates the mechanisms of Bdph for twitch facilitation in ICR mouse vas deferens (MVD). Materials and methods: Electrical field stimulation (EFS, supramaximal voltage ranging from 60–90 V, 1 ms, 0.2 Hz) was applied to the isolated MVD in Krebs solution. Interactions between Bdph (50 µM) and calcium antagonist (verapamil, diltiazem or aspaminol) on the EFS-evoked twitch responses were determined. The number of experiments was 3–18. Results: Bdph (50 µM)-induced twitch facilitations from 100 to 391.9% were unrelated to activation of postjunctional cholinergic or adrenergic receptors. Verapamil and Bdph unabolished the twitch facilitation each other. Diltiazem unabolished the Bdph-induced twitch facilitation. In contrast, Bdph abolished those induced by diltiazem. Aspaminol at 20 μM abolished the Bdph-induced twitch facilitation. In contrast, Bdph abolished those induced by aspaminol. Tetraethylammonium and 4-aminopyridine, the K+ channel blockers, significantly augmented the Bdph-induced twitch facilitation. Discussion and conclusions: Bdph may bind to the different, more and same subtypes of VDCCs from verapamil, than diltiazem, and as aspaminol does on prejunctional membrane, respectively. Besides a blocker of VDCCs, Bdph may be a blocker of K+ channels on prejunctional membrane. Thus, Bdph depolarized the membrane and facilitated the cumulative Ca2+-induced twitch responses.

Abstract In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

The virulence of genotype I (GI) Japanese encephalitis virus (JEV) is under debate. We investigated differences in the virulence of GI and GIII JEV by calculating asymptomatic ratios based on serologic studies during GI- and GIII-JEV endemic periods. The results suggested equal virulence of GI and GIII JEV among humans.

Abstract Background We recently reported that hesperetin-5,7,3’-O-triacetate (HTA) dually inhibited phosphodiesterase (PDE)3/4 with a therapeutic ratio of 20.8. The application and development of PDE4 inhibitors for treating asthma or COPD are limited by their side effects, such as nausea, vomiting and gastric hypersecretion. PDE4 inhibitors were reported to reverse xylazine/ketamine-induced anesthesia in rats and triggered vomiting in ferrets. Thus the reversing effect of HTA on xylazine/ketamine-induced anesthesia in mice was studied to assess emetic effect of HTA. The aim of this study was to prove the therapeutic effect of HTA without vomiting effect at an effective dose for treating COPD. Methods Ten female BALB/c mice in each group were sensitized by ovalbumin (OVA) on days 0 and 14. On day 21, these mice were emphasized the sensitization by Freund’s complete adjuvant. Mice were challenged by 1% OVA nebulization on days 28, 29, and 30. Airway hyperresponsiveness (AHR) was assessed on day 32 in each group, using the FlexiVent system to determine airway resistance (RL) and lung dynamic compliance (Cdyn) in anesthetized ovalbumin (OVA)-sensitized and challenged mice. Each group was orally administered HTA (10 ~ 100 μmol/kg), roflumilast (1 and 5 mg/kg) or vehicles (controls) 2 h before and 6 and 24 h after OVA provocation. For comparison, sham-treated mice were challenged with saline instead of 1% OVA. The ability to reverse xylazine/ketamine-induced anesthesia by HTA or roflumilast for 3 h was determined in normal mice. We used roflumilast, a selective PDE4 inhibitor and bronchodilator for severe COPD approved by the US Food and Drug Administration, as a reference drug. Results In the results, HTA (100 μmol/kg, p.o.) or roflumilast (5 mg/kg, p.o.) significantly suppressed all RL values of MCh at 0.78 ~ 25 mg/mL and enhanced Cdyn values of MCh at 3.125 ~ 25 mg/mL compared to OVA-sensitized and -challenged control mice. Orally administered 1, 3 or 10 mg/kg roflumilast, but not 30 or 100 μmol/kg HTA, significantly reversed xylazine/ketamine-induced anesthesia. Conclusions In contrast to roflumilast, HTA may ameliorate COPD but induce few side effects of nausea, vomiting and gastric hypersecretion at an effective dose for treating COPD, because HTA did not reverse xylazine/ketamine-induced anesthesia in mice.

The aim of this paper is to enrich random fixed point theory, which is one of the cornerstones of probabilistic functional analysis. In this paper, we introduce the notions of random, comparable MT- γ contraction and random, comparable Meir-Keeler contraction in the framework of complete random metric spaces. We investigate the existence of a random fixed point for these contractions. We express illustrative examples to support the presented results.

In this manuscript, we introduce a new type of contraction, bilateral contraction which merges two significant approaches in the fixed point theory: Caristi type contractions and Jaggi type contractions. The principal aim of the main result is to enrich the literature by combining the techniques of the mentioned two celebrated results that belong to Jaggi and Caristi. We consider an example to indicate the validity and genuine nature of the main result.

In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to indicate the validity of the presented results. Our results unify and generalize a number of best proximity point results on the topic in the corresponding recent literature.

In this paper, we initiate the concept of interpolative Ćirić-Reich-Rus type contractions via the Branciari distance and prove some related fixed points results for such mappings. Moreover, an example is provided to show the useability of our obtained results.

We study a new family of functions Q(X,Y), research its properties, and get some fixed point theorems about this family.

We introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems which also solves an optimization problem.

Theta (6-12 Hz) rhythmicity in the local field potential (LFP) reflects a clocking mechanism that brings physically isolated neurons together in time, allowing for the integration and segregation of distributed cell assemblies. Variation in the theta signal has been linked to locomotor speed, sensorimotor integration as well as cognitive processing. Previously, we have characterized the relationship between locomotor speed and theta power and how that relationship varies across the septotemporal (long) axis of the hippocampus (HPC). The current study investigated the relationship between whole body acceleration, deceleration and theta indices at CA1 and dentate gyrus (DG) sites along the septotemporal axis of the HPC in rats. Results indicate that whole body acceleration and deceleration predicts a significant amount of variability in the theta signal beyond variation in locomotor speed. Furthermore, deceleration was more predictive of variation in theta amplitude as compared to acceleration as rats traversed a linear track. Such findings highlight key variables that systematically predict the variability in the theta signal across the long axis of the HPC. A better understanding of the relative contribution of these quantifiable variables and their variation as a function of experience and environmental conditions should facilitate our understanding of the relationship between theta and sensorimotor/cognitive functions.

We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.

By using the weaker Meir-Keeler function ϕ and the triangular α-admissible mapping α, we introduce the notion of (α-ϕ)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.

We establish some fixed point theorems for α-admissible mappings in the context of metric-like space via various auxiliary functions. In particular, we prove the existence of a fixed point of the generalized Meir-Keeler type α-ϕ-contractive self-mapping f defined on a metric-like space X. The given results generalize, improve, and unify several fixed point theorems for the generalized cyclic contractive mappings that have appeared recently in the literature.

We introduce the notions of (α-ϕ-ψ)-weaker Meir-Keeler contractive mappings and (α-φ)-stronger Meir-Keeler contractive mappings. We discuss the existence of periodic points in the setting of generalized quasi-metric spaces. Our results improve, extend, and generalize several results in the literature.

We introduce the notion of generalized weaker (α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

We prove new coincidence point theorems for the -contractions and generalized Meir-Keeler-type --contractions in partially ordered metric spaces. Our results generalize many recent coincidence point theorems in the literature.

We prove two new fixed point theorems in the framework of partially ordered metric spaces. Our results generalize and improve many recent fixed point theorems in the literature.

We introduce the notion of weaker (ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

For a tvs-G-cone metric space (𝑋,𝐺) and for the family 𝒜 of subsets of X, we introduce a new notion of the tvs-ℋ-cone metric ℋ with respect to G, and we get a fixed result for the 𝒞ℬ𝒲-tvs-G-cone-type function in a complete tvs-G-cone metric space (𝒜,ℋ). Our results generalize some recent results in the literature.

The purpose of this paper is to present the fixed points and endpoints of set-valued contractions concerning with the stronger Meir-Keeler cone-type mappings in cone metric spcaes. Our results generalize the recent results of Kadelburg and Radenović, 2011; Wardowski, 2009.

By using the stronger Meir-Keeler mapping, we introduce the concepts of the sMK-G-cyclic mappings, sMK-K-cyclic mappings, and sMK-C-cyclic mappings, and then we prove some best proximity point theorems for these various types of contractions. Our results generalize or improve many recent best proximity point theorems in the literature (e.g., Elderd and Veeramani, 2006; Sadiq Basha et al., 2011).

We introduce the notions of the 𝒲 function and 𝒮 function, and then we prove two common fixed point theorems in complete generalized metric spaces under contractive conditions with these two functions. Our results generalize or improve many recent common fixed point results in the literature.

We obtain some new fixed point theorems for 𝜓-contractive mappings in ordered metric spaces. Our results generalize or improve many recent fixed point theorems in the literature (e.g., Harjani et al., 2011 and 2010).

We obtain some new fixed point theorems for a (𝜓,𝜙)-pair Meir-Keeler-type set-valued contraction map in metric spaces. Our main results generalize and improve the results of Klim and Wardowski, (2007).

We introduce the notions of the asymptotic SMK-sequence with respect to the stronger Meir-Keeler cone-type mapping ξ:int(P)∪{θ}→[0,1) and the asymptotic WMK-sequence with respect to the weaker Meir-Keeler cone-type mapping ϕ:int(P)∪{θ}→int(P)∪{θ} and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone P. Our results generalize some recent results.

We use a concept of abstract convexity to define the almost S-KKM𝒞 property, al-S-KKM𝒞(X,Y) family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors.

We establish some coincidence theorems, generalized variational inequality theorems, and minimax inequality theorems for the family G-KKM(X,Y) and the Φ-mapping on G-convex spaces.

We proved two common fixed point theorems for four self-mappings and two set-valued mappings with φ-contractive condition in a Menger space.