Contractible Research Articles

Topological Interactions Between Homotopy and Dehn Twist Varieties

The topological Dehn twists have several applications in mathematical sciences as well as in physical sciences. The interplay between homotopy theory and Dehn twists exposes a rich set of properties. This paper generalizes the Dehn twists by proposing the notion of pre-twisted space, orientations of twists and the formation of pointed based space under a homeomorphic continuous function. It is shown that the Dehn twisted homotopy under non-retraction admits a left lifting property (LLP) through the local homeomorphism. The LLP extends the principles of Hurewicz fibration by avoiding pullback. Moreover, this paper illustrates that the Dehn twisted homotopy up to a base point in a based space can be formed by considering retraction. As a result, two disjoint continuous functions become point-wise continuous at the base point under retracted homotopy twists. Interestingly, the oriented Dehn twists of a pre-twisted space under homotopy retraction mutually commute in a contractible space.

Formal contracts mitigate social dilemmas in multi-agent reinforcement learning

Multi-agent Reinforcement Learning (MARL) is a powerful tool for training autonomous agents acting independently in a common environment. However, it can lead to sub-optimal behavior when individual incentives and group incentives diverge. Humans are remarkably capable at solving these social dilemmas. It is an open problem in MARL to replicate such cooperative behaviors in selfish agents. In this work, we draw upon the idea of formal contracting from economics to overcome diverging incentives between agents in MARL. We propose an augmentation to a Markov game where agents voluntarily agree to binding transfers of reward, under pre-specified conditions. Our contributions are theoretical and empirical. First, we show that this augmentation makes all subgame-perfect equilibria of all Fully Observable Markov Games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we show that for general contract spaces, and even under partial observability, richer contract spaces lead to higher welfare. Hence, contract space design solves an exploration-exploitation tradeoff, sidestepping incentive issues. We complement our theoretical analysis with experiments. Issues of exploration in the contracting augmentation are mitigated using a training methodology inspired by multi-objective reinforcement learning: Multi-Objective Contract Augmentation Learning. We test our methodology in static, single-move games, as well as dynamic domains that simulate traffic, pollution management, and common pool resource management.

Left Atrial Strain to Predict Postoperative Atrial Fibrillation in Patients Undergoing Off-pump Coronary Artery Bypass Graft

ObjectivePostoperative atrial fibrillation (POAF) is associated with increased morbidity, mortality, and length of stay. The objective of this study was to assess the utility of left atrial strain (LAS) to predict POAF in patients undergoing off pump coronary artery bypass grafting (OPCABG). DesignRetrospective Observational Study. SettingTertiary Care Level Hospital. Participants103 undergoing OPCABG. InterventionsNone. Measurements and ResultsIn addition to comprehensive TTE, LAS was measured for reservoir (R), conduction (CD), and contraction (CT) components. The POAF was defined as new electrocardiography evidence of AF requiring treatment. Logistic regression was done to assess the factors associated with POAF. The diagnostic accuracy of variables in predicting POAF was assessed by ROC analysis.POAF was documented in 24 (23.3%) patients. There was no difference in EF, average GLS and proportion of LVDD grades between patients with POAF and patients without POAF. All the three components of LAS: LAS R (19.2 ± 4.7 vs 23.5 ± 4.8; p<0.001), LAS CD (8.9 ± 3.7 vs 12.3 ± 4.8; p=0.1) and LAS CT (10.3 ± 3.9 vs 12.1 ± 4.1; p=0.04) were significantly lower among patients with POAF as compared to patients without POAF respectively. According to univariate analysis, all components of LAS were found to be statistically significant predictors of POAF. On multivariate analysis, only age (OR=1.08; p=0.025) and LAS R (OR=0.84; p=0.004) were independently associated with POAF. The LAS R was a better predictor of POAF with AUC of 0.758, than LAS CD (AUC=0.67) and LAS CT (AUC=0.62). The LAS R had optimal cut-off of 23% with sensitivity of 95.8% (C.I. 78.9%- 99.9%) and specificity of 49.4% (37.9%- 60.9%) to predict POAF. ConclusionsLAS R is significant predictor of POAF and its use can be recommended for screening of OPCABG patients at high risk of POAF.

Fixed-Point Theorems for Fuzzy Mappings

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra.

Bridgeland stability conditions and skew lines on ℙ3

Inspired by Schmidt’s work on twisted cubics, we study wall crossings in Bridgeland stability, starting with the Hilbert scheme Hilb 2 m + 2 ( P 3 ) parametrizing pairs of skew lines and plane conics union a point. We find two walls. Each wall crossing corresponds to a contraction of a divisor in the moduli space and the contracted space remains smooth. Building on work by Chen–Coskun–Nollet, we moreover prove that the contractions are K-negative extremal in the sense of Mori theory and so the moduli spaces are projective.

AR EXPLORATION OF THE PERSPECTIVE/ARCHITECTURAL SPACE PAINTED BY PERUGINO

Abstract. The perspective study of one of the panels from the cycle of San Bernardino attributed to Perugino has revealed a contracted space in depth, represented three-dimensionally by the objective model. In contrast, the ideal model eliminates the contraction and maintains the proportions dictated by the architectural interpretation. The contribution presents an advancement in the perspective study aimed at developing an augmented reality (AR) application. It is designed to be experienced at the museum housing the artwork, serving as an in-depth exploration that explains to visitors the nature of the perspective space and the architectural space represented. The case study of the painting by Perugino becomes an opportunity to define and experiment with a workflow aimed at creating AR applications focused on the visualisation of architectural models derived from the perspective restitution of pictorial works. The description of the adopted method focuses on the following aspects: the use of the pictorial image as an AR marker and the relationship between the perspective picture plane and the 3D model; the optimisation of 3D models for AR visualisation purposes; the issue of the landscape; scene lighting; and the user interface for multilayer interaction.

The cyber-industrialization of catfishing and romance fraud

We examine a new form of online fraud, which we refer to as Intimacy Manipulated Fraud Industrialization (IMFI). This type of fraud bears a strong resemblance to traditional online romance fraud and catfishing, but is “industrialized” through enterprise business practices, software platforms, and customer service processes. To gain a better understanding of this operation, we conducted an inductive analysis of publicly available testimonial and review data provided by current and prior employees of a specific company in the online customer service contract space. Companies hire individuals online to work as “chat moderators” or “customer service providers” who are told that their task is to advance engagement on social media platforms. In fact, they are being recruited as “sexting” workers, paid on a per-text basis to engage in intimate chatting with clients who believe they're interacting with individuals of the opposite gender on a dating site. The process is mediated via client management processes that monitor employee productivity and monetize all interactions between “clients” and “workers.” The company executes these processes with great efficiency by algorithmically assigning multiple workers to individual clients and assembling background files on clients in real time. We find that workers serve as both exploiters of their clients as well as victims of the company they work for. The implications of our study could significantly impact how we address AI-generated online fraud in the future, shedding light on the complex dynamics at play within these fraudulent enterprises.

Random simple-homotopy theory

We implement an algorithm RSHT (random simple-homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions. For triangulated d-manifolds with d≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 6$$\\end{document}, we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex triangulation of the Abalone, and more generally, (14k+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(14k+1)$$\\end{document}-vertex triangulations of a new series of Bing’s houses with k rooms, k≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k\\ge 3$$\\end{document}, which all can be deformed to a point using only six pure elementary expansions.

Porous Co3O4/VS4/rGO-SDBS@NF nanoflower as a high performance supercapacitor electrode

Maximizing the performance of supercapacitors requires the design of high-conductivity, stable, and cost-effective electrode materials. The current study presents a novel solution in the form of self-supporting binder-free hierarchical Co3O4/VS4/rGO-SDBS@NF composite electrodes. These electrodes are fabricated using a facile and efficient two-step hydrothermal process. The growth of Co3O4 particles on VS4/rGO-SDBS flower-shaped nanosheet arrays on nickel foam substrates results in a sufficient contraction and expansion space distribution during charge and discharge. The Co3O4/VS4/rGO-SDBS@NF composite shows a specific capacitance of 2620 F g−1 at 1 A g−1, which is significantly compared to the VS4/rGO-SDBS@NF composite at 284 F g−1 in a 6 M KOH solution. Furthermore, the as-grown electrode Co3O4/VS4/rGO-SDBS@NF composite displays excellent cycling stability, with 97.4 % of its initial capacitance retained after 5000 cycles. In summary, the utilization of a simple and accessible manufacturing and synthesis method, absence of binders, in-situ growth technique, achievement of a special morphology with effective electrochemistry, excellent supercapacitor capacity, and high cyclic stability demonstrate significant improvements compared to recent works. These results provide a new perspective for the selection and synthesis of materials and the design and fabrication of electrodes for supercapacitors as energy storage devices.

Fixed point sets and the fundamental group I: semi-free actions on G-CW-complexes

Smith theory says that the fixed point set of a semi-free action of a group $G$ on a contractible space is ${\mathbb {Z}}_p$ -acyclic for any prime factor $p$ of the order of $G$ . Jones proved the converse of Smith theory for the case $G$ is a cyclic group acting semi-freely on contractible, finite CW-complexes. We extend the theory to semi-free group actions on finite CW-complexes of given homotopy types, in various settings. In particular, the converse of Smith theory holds if and only if a certain $K$ -theoretical obstruction vanishes. We also give some examples that show the geometrical effects of different types of $K$ -theoretical obstructions.

Green Hyperbolic Complexes on Lorentzian Manifolds

We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyperbolic complexes through a generalization of retarded and advanced Green’s operators, called retarded and advanced Green’s homotopies, which are shown to be unique up to a contractible space of choices. We prove homological generalizations of the most relevant features of Green hyperbolic operators, namely that (1) the retarded-minus-advanced cochain map is a quasi-isomorphism, (2) a differential pairing (generalizing the usual fiber-wise metric) on a Green hyperbolic complex leads to covariant and fixed-time Poisson structures and (3) the retarded-minus-advanced cochain map is compatible with these Poisson structures up to homotopy.

330 Interactions of Brain, Blood, and CSF: A Novel Mathematical Model of Cerebral Edema

INTRODUCTION: Previous models of intracranial pressure (ICP) dynamics have not included flow of cerebral interstitial fluid (ISF) and changes in resistance to its flow when brain swelling occurs. METHODS: We developed a lumped parameter model which includes a representation of cerebral ISF flow within brain tissue and its interactions with CSF flow and CBF. The model is based on an electrical analog circuit with four intracranial compartments: the (1) subarachnoid space, (2) brain, (3) ventricles and (4) cerebral vasculature. We determined changes in pressure and volume within cerebral compartments at steady-state and simulated perturbations: Rapid injection into the intracranial space, hyper-and hypoventilation. We simulated changes in resistance to flow or absorption of CSF and cerebral ISF to model hydrocephalus and cerebral edema. RESULTS: The model accurately replicates features of intracranial physiology including the pressure–volume curve, increased ICP pulse pressure with rising ICP, hydrocephalus from increased resistance to CSF outflow, and changes associated with ventilation. Importantly, modeling edema with increased resistance to ISF flow mimics key features of brain swelling including elevated ICP, increased brain volume, effaced ventricles, and a contracted subarachnoid space. Similarly, decreased resistance to flow of fluid across the BBB leads to an exponential-like rise in ICP and ventricular collapse. CONCLUSIONS: The model accurately depicts the complex interactions that occur between pressure, volume, and resistances to flow in the different intracranial compartments under specific pathophysiological conditions. In modelling resistance to bulk flow of cerebral ISF, it may serve as a platform for improved modelling of cerebral edema and blood–brain barrier disruption that occur following brain injury.

Neuromuscular fatigability of plantar flexors following continuous and intermittent contractions.

The purpose of this study is to investigate if a continuous muscle contraction (CON) is more fatiguing than an intermittent exercise (INT) performed until task failure. To get a more comprehensive picture of neuromuscular fatigability, in addition to the commonly used maximal voluntary contraction (MVC), we assessed the maximal torque sustainability (i.e., the ability to maintain a high level of torque for 1 min). Fourteen subjects performed a plantar flexors MVC of 1-min duration (MVC1-MIN) before and after CON or INT contractions at 40% MVC until task failure. Despite a greater torque-time integral for the INT task, a similar MVC reduction was found after both exercises. On the contrary, a greater torque loss during the MVC1-MIN was observed after the CON exercise and it was positively correlated to the mean exercise torque. These results reveal that, for exercises performed until exhaustion, the contraction pattern (i.e., CON vs. INT) affects the ability to maintain a high level of torque, but does not influence the maximal torque production capacity. Thus, we demonstrate that maximal torque production and sustainability are two distinct and complementary characteristics of neuromuscular fatigability. Consequently, when considering both capacities, it results that, an exhausting CON contraction is more fatiguing than an exhausting INT effort. This highlights the importance of simultaneously evaluating both capacities when exploring neuromuscular fatigability.NEW & NOTEWORTHY This study provides new information about the influence of the contraction pattern (i.e., continuous and intermittent) on the development of neuromuscular fatigability when exercise is performed until exhaustion. Maximal torque production is similarly reduced by both exercises, whereas maximal torque sustainability is impaired only after the continuous exercise. To evaluate neuromuscular fatigability, we then recommend using a sustained maximal voluntary contraction since this measure allows to concurrently collect information on complementary aspects of neuromuscular fatigability.

Cybersecurity and Ethereum Security Vulnerabilities Analysis

As computer technology develops, the popularity of cryptocurrencies and their use will grow, and the newer people enter the industry. It changes the business model between organized businesses out of the need for another trusted party. Blockchain smart contracts can automatically enforce agreed contract between two unknowns. Briefly introduce Ethereum, a cryptocurrency, and focus on the security of its smart contracts in internet transactions. Ethereum was the first platform to support high-level programming languages to implement smart contracts, and the second largest blockchain platform, providing a runtime environment for essentially all Decentralized Finance applications. Bitcoin also supports the development and execution of smart contracts, but it is affected by the nature of the programming language used, and it hardly supports transactions except for verifying signatures. Because smart contracts can support a variety of large transactions, some security vulnerabilities can be extremely costly. In an extensive search and survey, the issue of smart contracts for the Ethereum blockchain was valued. The article will discuss some of the existing or former contract vulnerabilities and their solutions. It concludes with a discussion of the future direction of the smart contract space and provides some suggestions for those researching the field.

Contractibility of homogeneous Kenmotsu manifolds

We prove that every homogeneous Kenmotsu manifold is a contractible space.

When is the space of semi-additive functionals an absolute (neighbourhood) retract?

In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp(X) is a contractible compact space then the space OSf(X) is also a contractible compact space. As a consequence it is established that the space OSf(X) of semi-additive functionals is absolute (neighbourhood) retract if and only if the hyperspace exp(X) is so.

Nonmanifold monodromy spaces of branched coverings between manifolds

By a construction of Berstein and Edmonds every proper branched cover f between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of f to the target manifold. For proper branched covers between 2-manifolds the monodromy space is known to be a manifold. We show that this does not generalize to dimension 3 by constructing a self-map of the 3-sphere for which the monodromy space is not a locally contractible space.

RE-3DLVNet: Refined estimation of the left ventricle volume via interactive 3D segmentation and reinforced quantification

The reliable estimation of left ventricle (LV) volume from 3D medical data enables both visible shape exhibition and accurate volume report, for efficiently clinical cardiac diagnosis. However, it is still open challenging as: 1) intermediate volume error caused by fully depending on segmentation, 2) non-visualized result via solo using direct regression, 3) ambiguous conclusion from the unmatching multi-type outputs, 4) large spatial scene of stereo domain, 5) unbalanced information in 3D medical data between depth and slice plane, 6) large regression output space. We proposed RE-3DLVNet the first powerful work for the refined volume estimation of 3D LV in a novel way segmentation volume±reinforced volume. It uses segmentation with advantage of intuitive voxel-to-voxel optimization to fast stabilize a rough volume. Reciprocally, it makes reinforced quantification (ReinQuan) with advantage of global inference to focus on checking scene misunderstanding and precisely remedy accumulative error caused by massive local optimization, for refining the volume. 1) In segmentation, a probe convolution creatively perceives global scene distribution, and a low-to-high depth segmentation net with high depth connection releases latent structure in low-resolution depth. 2) In ReinQuan, a regression net is conducted to refine estimating the reinforced volume of the segmentation, with focused contracted output space. 3) Interactively, a consistent constraint transfers the ReinQuan deviation between segmented result and its ground truth for penetratively penalizing. Extensive experiments show RE-3DLVNet clinical potential in assessing cardiac function and anatomy. It 1) enables exact 3D LV volume estimation with mean absolute error down to 1.03ml, increasing measurement precise by 30.41% compared to segmentation volume, and 2) achieves accurate visualization segmentation with Dice coefficient up to 95.13%.

On Fuzzy F ∗ -Simply Connected Spaces in Fuzzy F ∗ -Homotopy

In this paper, the notions of fuzzy F ∗ -simply connected spaces and fuzzy F ∗ -structure homeomorphisms are introduced, and further fuzzy F ∗ -structure homeomorphism between fuzzy F ∗ -path-connected spaces are studied. Also, it is shown that every fuzzy F ∗ -structure subspace of fuzzy F ∗ -simply connected space is fuzzy F ∗ -simply connected subspace. Further, the concepts of fuzzy F ∗ -contractible spaces and fuzzy F ∗ -retracts are introduced, and it is proved that every fuzzy F ∗ -contractible space is fuzzy F ∗ -simply connected.

Order batching and order picking with 3D positioning of the articles: solution through a hybrid evolutionary algorithm.

A critical factor in the logistic management of firms is the degree of efficiency of the operations in distribution centers. Of particular interest is the pick-up process, since it is the costliest operation, amounting to 50 and up to 75% of the total cost of the activities in storage facilities. In this paper we jointly address the order batching problem (OBP) and the order picking problem (OPP). The former problem amounts to find optimal batches of goods to be picked up, by restructuring incoming orders by either splitting up large orders or combining small orders into larger ones that can then be picked in a single picking tour. The OPP, in turn, involves identifying optimal sequences of visits to the storage positions in which the goods to be included in each batch are stored. We seek to design a plan that minimizes the total operational cost of the pick-up process, proportional to the displacement times around the storage area as well as to all the time spent in pick-ups and finishing up orders to be punctually delivered. Earliness or tardiness will induce inefficiency costs, be it because of the excessive use of space or breaches of contracts with customers. Tsai, Liou and Huang in 2008 have generated 2D and 3D instances. In previous works we have addressed the 2D ones, achieving very good results. Here we focus on 3D instances (the articles are placed at different levels in the storage center), which involve a higher complexity. This contributes to improve the performance of the hybrid evolutionary algorithm (HEA) applied in our previous works.