Unique Lifting Research Articles

Monoidal strengthening and unique lifting in MIQCPs

Monoidal strengthening and unique lifting in MIQCPs

Optimization of Elevator Usage by Image Processing for Optimal Energy Conservation

An efficient vertical transit system is a crucial feature of contemporary office buildings. Modern machine learning (ML) algorithms make it simple to optimise lift control strategies. This study proposes a revolutionary way to use Raspberry Pi camera module data for the best possible dispatching of traditional passenger lifts. It is assumed that an image processing system processes a real-time video to ascertain the quantity of people and objects utilising the lifts and waiting for a lift vehicle in the halls. These numbers are assumed to be connected to a specific uncertain probability. The efficiency of our unique lift control algorithm is derived from the need to serve a crowded floor completely, sending as many lifts as possible there and filling them to the maximum weight permitted, in addition to the probabilistic utilisation of the number of people and/or items waiting. The suggested technique introduces the idea of the effective number of persons and items to account for the uncertainty that may arise from the image processing system's imperfection. Reducing wait time, energy conservation and optimization are main the goals of this research. The proposed approach was implemented, and the simulation results showed that the passenger journey time was reduced. A three-story office building was the intended application for the prototype model. Key Words: Elevator, Raspberry Pi, Machine Learning, Optimization, Image Processing

Obstruction theory and the level n elliptic genus

Given a height at most two Landweber exact $\mathbb {E}_\infty$-ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the Ando criterion admits a unique lift to an $\mathbb {E}_\infty$-complex orientation $\mathrm {MU} \to E$. As a consequence, we give a short proof that the level $n$ elliptic genus lifts uniquely to an $\mathbb {E}_\infty$-complex orientation $\mathrm {MU} \to \mathrm {tmf}_1 (n)$ for all $n\, {\geq}\, 2$.

Machine Learning Derived Lifting Technique in People without Low Back Pain.

This paper presents a method for determining the number of lifting techniques used by healthy individuals through the analysis of kinematic data collected from 115 participants utilizing an motion capture system. The technique utilizes a combination of feature extraction and Ward's method to analyse the range of motion in the sagittal plane of the knee, hip, and trunk. The findings identified five unique lifting techniques in people without low back pain. The multivariate analysis of variance statistical analysis reveals a significant difference in the range of motion in the trunk, hip and knee between each cluster for healthy people (F (12, 646) = 125.720, p < 0.0001).Clinical Relevance- This information can assist healthcare professionals in choosing effective treatments and interventions for those with occupational lower back pain by focusing rehabilitation on specific body parts associated with problematic lifting techniques, such as the trunk, hip, or knee, which may lead to improved pain and disability outcomes, exemplifying precision medicine.

Parsing as a lifting problem and the Chomsky-Sch\"utzenberger representation theorem

We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more general notion of CFG over any category $C$, defined as a finite species $S$ equipped with a color denoting the start symbol and a functor of operads $p : Free[S] \to W[C]$ into the operad of spliced arrows in $C$. We show that many standard properties of CFGs can be formulated within this framework, and that usual closure properties of CF languages generalize to CF languages of arrows. We also discuss a dual fibrational perspective on the functor $p$ via the notion of "displayed" operad, corresponding to a lax functor of operads $W[C] \to Span(Set)$. We then turn to the Chomsky-Sch\"utzenberger Representation Theorem. We describe how a non-deterministic finite state automaton can be seen as a category $Q$ equipped with a pair of objects denoting initial and accepting states and a functor of categories $Q \to C$ satisfying the unique lifting of factorizations property and the finite fiber property. Then, we explain how to extend this notion of automaton to functors of operads, which generalize tree automata, allowing us to lift an automaton over a category to an automaton over its operad of spliced arrows. We show that every CFG over a category can be pulled back along a ND finite state automaton over the same category, and hence that CF languages are closed under intersection with regular languages. The last important ingredient is the identification of a left adjoint $C[-] : Operad \to Cat$ to the operad of spliced arrows functor, building the "contour category" of an operad. Using this, we generalize the C-S representation theorem, proving that any context-free language of arrows over a category $C$ is the functorial image of the intersection of a $C$-chromatic tree contour language and a regular language.

On maps with continuous path lifting

We study a natural generalization of covering projections defined in terms of unique lifting properties. A map $p:E\to X$ has the <em>continuous path-covering property</em> if all paths in $X$ lift uniquely and continuously (rel. basepoint) with respect t

Polyhedra, lattice structures, and extensions of semigroups

For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of the associated pair of semigroups. Being free for the pair of semigroups is equivalent to flatness for the corresponding algebras. Our main result is phrased in this dual setup: the category of free extensions always contains an initial object, which we describe explicitly. These objects seem to be related to unique liftings in log geometry. Further motivation comes from the deformation theory of the associated toric singularity.

Unsteady Aerodynamics Around a Pitching Airfoil with Shock and Shock-Induced Boundary-Layer Separation

This study numerically investigated the characteristics of unsteady aerodynamic forces around a pitching airfoil in the transonic flow regime. The unsteady Reynolds-averaged compressible Navier–Stokes (URANS) equations were solved using a Spalart–Allmaras (SA) turbulence model. The pitching NACA64A010 airfoil at mean angles of attack of 0, 2, 4, and 6 deg with the amplitude of 1 deg and reduced frequency of 0.2 was parametrically simulated. The study found that the trend of the unsteady aerodynamic characteristics around the pitching airfoil, particularly that of the unsteady lift force, significantly changes with the mean-angle-of-attack conditions. The shock-induced boundary-layer separation and reattachment during the pitching oscillation have a crucial role in determining the trend of the unsteady aerodynamic forces, such as the phase-delayed or phase-advanced features for the variation in the angle of attack. The boundary-layer separation during the oscillation, observed at a high mean angle of attack of 6 deg, produces the phase-advanced feature of the lift force. Because the phase-advanced feature is associated with a positive damping effect, the result indicates that the boundary-layer separation may serve as a stabilizing effect on the pitching airfoil motion. The boundary-layer reattachment from separation during the airfoil oscillation, observed at an intermediate mean angle of attack of 4 deg, generates an unusual shock wave movement, resulting in a unique lift loop for the variation in the angle of attack. The study also demonstrated a good prediction accuracy of the URANS with the SA model for the unsteady aerodynamics around the pitching airfoil with the shock and shock-induced boundary-layer separation.

THE STUDY OF A JIB CRANE FROM A CARGO SHIP

This paper presents the study of a jib crane from a general cargo ship. There are numerous different types of vessels operating today in the various markets worldwide. Besides, thousands of cargo vessel ply the world’s oceans and seas each year, handling the bulk of international trade. The cranes from cargo ship is required to be adequate stability and strength for each load. All cranes from vessel are mounted on deck of the ship. Having regard in particular to the stress induced at its mounting or fixing points, adequately ballasted, securely anchored and supported by outriggers as necessary to ensure its stability when lifting. A jib from a crane from cargo ship is a type of overhead lifting device that is often used in a smaller work cell area for repetitive and unique lifting tasks. The extreme values of the stresses and reaction forces are determined by the finite element method. In this manuscript, the design of the cargo ship and the study of a jib crane are made using NX software from Siemens.

Introducing POLYPUS: A novel adaptive vacuum gripper

Underactuated grippers represent an appealing solution that allows complex objects to be grasped and manipulated via passive adaptation of the hand with objects via simple control inputs. The grasping ability can be further improved in combination with vacuum gripping, i.e., by outfitting the gripper phalanges with suction cups, that remains a largely underinvestigated solution. This paper presents a novel gripper, referred to as POLYPUS, that features underactuation and vacuum grasping to handle uneven and even objects made of different materials, including cardboard, glass, sheet metal, and plastic. Being characterized by a solid frame, POLYPUS does not fall in the soft gripper category, while preserving similar adaptability. It provides unique load lifting capacity that ranges from light to heavy objects, whereas most of the existing grippers are tailored for a specific target payload. Being modular in design, POLYPUS can be easily reconfigured for a wide range of object sizes and applications. Results obtained from an extensive set of simulations are included to evaluate the grasping performance expressed in terms of the minimum suction force to handle objects of varying shape, material, and pose.

The Most Refined Axiom for a Digital Covering Space and Its Utilities

This paper is devoted to establishing the most refined axiom for a digital covering space which remains open. The crucial step in making our approach is to simplify the notions of several types of earlier versions of local (k0,k1)-isomorphisms and use the most simplified local (k0,k1)-isomorphism. This approach is indeed a key step to make the axioms for a digital covering space very refined. In this paper, the most refined local (k0,k1)-isomorphism is proved to be a (k0,k1)-covering map, which implies that the earlier axioms for a digital covering space are significantly simplified with one axiom. This finding facilitates the calculations of digital fundamental groups of digital images using the unique lifting property and the homotopy lifting theorem. In addition, consider a simple closed k:=k(t,n)-curve with five elements in Zn, denoted by SCkn,5. After introducing the notion of digital topological imbedding, we investigate some properties of SCkn,5, where k:=k(t,n),3≤t≤n. Since SCkn,5 is the minimal and simple closed k-curve with odd elements in Zn which is not k-contractible, we strongly study some properties of it associated with generalized digital wedges from the viewpoint of fixed point theory. Finally, after introducing the notion of generalized digital wedge, we further address some issues which remain open. The present paper only deals with k-connected digital images.

Canonical lifts and $$\delta $$-structures

We extend the Serre–Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a p-adic formal scheme S. We show that the canonical lift is the unique lift to W(S) which admits a $$\delta $$ -structure in the sense of Joyal, Buium, and Bousfield. We prove analogous statements for families of ordinary p-groups and p-divisible groups.

Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains

We prove and apply two theorems: first, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schrödinger operator on a bounded or unbounded domain; second, a perturbation and lifting estimate for edges of the essential spectrum of a self-adjoint operator under a semi-definite perturbation. These two results are combined to obtain lower and upper Lipschitz bounds on the function parametrizing locally a chosen edge of the essential spectrum of a Schrödinger operator in dependence of a coupling constant. Analogous estimates for eigenvalues, possibly in gaps of the essential spectrum, are exhibited as well.

Fibrations, unique path lifting, and continuous monodromy

Given a path-connected space X and H≤π1(X,x0), there is essentially only one construction of a map pH:(X˜H,x˜0)→(X,x0) with connected and locally path-connected domain that can possibly have the following two properties: (pH)#π1(X˜H,x˜0)=H and pH has the unique lifting property. X˜H consists of equivalence classes of paths starting at x0, appropriately topologized, and pH is the endpoint projection. For pH to have these two properties, T1 fibers are necessary and unique path lifting is sufficient. However, pH always admits the standard lifts of paths.We show that pH has unique path lifting if it has continuous (standard) monodromies toward a T1 fiber over x0. Assuming, in addition, that H is locally quasinormal (e.g., if H is normal) we show that X is homotopically path Hausdorff relative to H. We show that pH is a fibration if X is locally path connected, H is locally quasinormal, and all (standard) monodromies are continuous.

Describing quasi-graphic matroids

The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and lifted-graphic matroids introduced earlier by Zaslavsky. For each biased graph (G,B) Zaslavsky defined a unique lift matroid L(G,B) and a unique frame matroid F(G,B), each on ground set E(G). We show that in general there may be many quasi-graphic matroids on E(G) and describe them all: for each graph G and partition (B,L,F) of its cycles such that B satisfies the theta property and each cycle in L meets each cycle in F, there is a quasi-graphic matroid M(G,B,L,F) on E(G). Moreover, every quasi-graphic matroid arises in this way. We provide cryptomorphic descriptions in terms of subgraphs corresponding to circuits, cocircuits, independent sets, and bases. Equipped with these descriptions, we prove some results about quasi-graphic matroids. In particular, we provide alternate proofs that do not require 3-connectivity of two results of Geelen, Gerards, and Whittle for 3-connected matroids from their introductory paper: namely, that every quasi-graphic matroid linearly representable over a field is either lifted-graphic or frame, and that if a matroid M has a framework with a loop that is not a loop of M then M is either lifted-graphic or frame. We also provide sufficient conditions for a quasi-graphic matroid to have a unique framework.Zaslavsky has asked for those matroids whose independent sets are contained in the collection of independent sets of F(G,B) while containing those of L(G,B), for some biased graph (G,B). Adding a natural (and necessary) non-degeneracy condition defines a class of matroids, which we call biased-graphic. We show that the class of biased-graphic matroids almost coincides with the class of quasi-graphic matroids: every quasi-graphic matroid is biased-graphic, and if M is a biased-graphic matroid that is not quasi-graphic then M is a 2-sum of a frame matroid with one or more lifted-graphic matroids.

Nonunique Lifting of Integer Variables in Minimal Inequalities

We explore the lifting question in the context of cut-generating functions. Most of the prior literature on this question focuses on cut-generating functions that have the unique lifting property. ...

Test map characterizations of local properties of fundamental groups

Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map defined in terms of unique lifting properties. The existence of generalized covering maps depends entirely on the verification of the unique path lifting property for a standard covering construction. Given any path-connected metric space [Formula: see text], and a subgroup [Formula: see text], we characterize the unique path lifting property relative to [Formula: see text] in terms of a new closure operator on the [Formula: see text]-subgroup lattice that is induced by maps from a fixed “test” domain into [Formula: see text]. Using this test map framework, we develop a unified approach to comparing the existence of generalized coverings with a number of related properties.

Some anomalous examples of lifting spaces

An inverse limit of a sequence of covering spaces over a given space X is not, in general, a covering space over X but is still a lifting space, i.e. a Hurewicz fibration with unique path lifting property. Of particular interest are inverse limits of finite coverings (resp. finite regular coverings), which yield fibrations whose fibre is homeomorphic to the Cantor set (resp. profinite topological group). To illustrate the breadth of the theory, we present in this note some curious examples of lifting spaces that cannot be obtained as inverse limits of covering spaces.

Deformation rings and parabolic induction

We study deformations of smooth mod $p$ representations (and their duals) of a $p$-adic reductive group $G$. Under some mild genericity condition, we prove that parabolic induction with respect to a parabolic subgroup $P=LN$ defines an isomorphism between the universal deformation rings of a supersingular representation $\bar{\sigma}$ of $L$ and of its parabolic induction $\bar{\pi}$. As a consequence, we show that every Banach lift of $\bar{\pi}$ is induced from a unique Banach lift of $\bar{\sigma}$.

Small loop transfer spaces with respect to subgroups of fundamental groups

Let H be a subgroup of π1(X,x0). In this paper, we extend the concept of X being SLT space to H-SLT space at x0. First, we show that the fibers of the endpoint projection pH:X˜H→X are a topological group when X is H-SLT space at x0 and H is a normal subgroup. Also, we show that under these conditions the concepts of homotopically path Hausdorff relative to H and homotopically Hausdorff relative to H coincide. Moreover, among other things, we show that the endpoint projection map pH has the unique path lifting property if and only if H is a closed normal subgroup of π1qtop(X,x0) when X is H-SLT at x0. Second, we present conditions under which the whisker topology agrees with the quotient of compact-open topology on X˜H. Also, we study the relationship between open subsets of π1wh(X,x0) and π1qtop(X,x0).