Linear identification of nonlinear systems: A lifting technique based on the Koopman operator

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to the socalled Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is "projected back" to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics.Comment: 6 page

Solving Sparse Integer Linear Systems

We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic complexity in terms of machine operations subject to a conjecture on the effectiveness of certain sparse projections. A LinBox-based implementation of this algorithm is demonstrated, and emphasizes the practical benefits of this new method over the previous state of the art

Lifted Worm Algorithm for the Ising Model

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energy estimator on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energy estimator on the complete graph, and leads to a significant constant improvement on toroidal grids.Comment: 9 pages, 6 figure

Chemical enhancement of footwear impressions in blood deposited on fabric — evaluating the use of alginate casting materials followed by chemical enhancement

Most footwear marks made in blood on a surface such as fabric tend to be enhanced in situ rather than physically recovered using a lifting technique prior to enhancement. This work reports on the use of an alginate material to recover the impressed footwear marks made in blood and deposited on a range of fabric types and colours. The lifted marks were then enhanced using acid black 1 and leuco crystal violet with excellent results. This presents a new method for the lifting and recovery of blood impressions in situ from crime scene followed by subsequent mark enhancement of the lifted impression

A case of mediastinal goiter treated surgically using a clavicle-lifting technique

AbstractIntroductionMediastinal goiter is a benign disease, which is defined as a goiter with the greater portion of its mass lying below the thoracic inlet. It is controversial whether the cervical approach is the best approach for all mediastinal goiter surgeries.Case presentationA 71-year-old woman presented with respiratory discomfort during exertion. Computed tomography (CT) revealed a mediastinal goiter extending to the arch of the aorta. Surgical resection was performed using a clavicle-lifting technique. The excised specimen was 13×10×5cm in size and weighed 220g. The pathological diagnosis was nodular goiter.DiscussionThe clavicle-lifting technique is a simple and safe technique that involves lifting the clavicles with a pediatric extension retractor (Kent Retractor Set, Takasago Medical Industry, Tokyo, Japan). This is a good choice for surgery on upper mediastinal lesions such as mediastinal goiters as it obviates the need for a median sternotomy.ConclusionAlthough further study is necessary, it appears that a transcervical approach using the clavicle-lifting technique may be an acceptable treatment for mediastinal goiters that extend to the aortic arch

Clip and snare lifting technique to assist cannulation of a papilla hidden behind a mucosal fold

No abstract availabl

Stabilization of (L,M) shift invariant plant

In this paper, a lifting technique is employed to realize a single input single output linear (L,M) shift invariant plant as a filter bank system. Based on the filter bank structure, a controller is designed so that the aliasing components in the control loop are cancelled and the loop gain becomes a time invariant transfer function. Pole placement technique is applied to stabilize the overall system and ensure the causality of the filters in the controller. An example on the control of a linear (L,M) shift invariant plant with simulation result is illustrated. The result shows that our proposed algorithm is simple and effective

Congruences between Hilbert modular forms: constructing ordinary lifts

Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension F'/F such that r|_{G_F'} has a modular lift which is ordinary at each place dividing l. We deduce a similar result for r itself, under the assumption that at places v|l the representation r|_{G_F_v} is reducible. This allows us to deduce improvements to results in the literature on modularity lifting theorems for potentially Barsotti-Tate representations and the Buzzard-Diamond-Jarvis conjecture. The proof makes use of a novel lifting technique, going via rank 4 unitary groups.Comment: 48 page

Sampling from a system-theoretic viewpoint: Part I - Concepts and tools

This paper is first in a series of papers studying a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. In this paper we present the paradigm and revise underlying technical tools, such as the lifting technique and some topics of the operator theory. This material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems, recovering many hitherto considered different solutions and leading to new results. Some of these applications are discussed in the second part

THE EFFECTS OF LOAD MASS ON THE KINEMATICS OF STIFF-LEGGED DEADLIFT

The purpose of this study was to investigate the effects of load mass on the kinematics of lower extremity joint movements during the stiff-legged deadlift (SLD) lift exercise. Five participants performed the SLD at 40%, 60%, and 80% of their estimated 1 repetition maximum. Measurements of the joint angle and angular velocity of the spine, hip, knee, and ankle were analyzed to understand the influence of various load masses in the SLD lifting technique. No statistical significant differences were found in the joint angles and angular velocities of the spine and lower extremity between different loads. Therefore, this study suggests that performing stiff-legged exercise up to 80% is safe to perform as long as the participants are experienced with this lifting technique