Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization Problems

In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well known that second-order optimality conditions involve the support function of the second-order tangent set. In this paper, we propose two approaches for establishing second-order optimality conditions for the nonconvex case. In the first approach, we extend the concept of the support function so that it is applicable to general nonconvex set-constrained problems, whereas in the second approach, we introduce the notion of the directional regular tangent cone and apply classical results of convex duality theory. Besides the second-order optimality conditions, the novelty of our approach lies in the systematic introduction and use, respectively, of directional versions of well-known concepts from variational analysis.

Enterprise IT Operations

Over the past decade or so, for most enterprises, information technology (IT) has shifted from being a support function to be a synonym for business wellness. During the same period, though, the scale and complexity of IT for running business has grown significantly; today, performing any business function requires complex interplay of many, often invisible and dynamically changing, technology components. This is making design resilient and interruption-free IT a significant challenge. This chapter discusses limitations of traditional approaches for managing enterprise IT operations; introduces the concept of cognitive automation, a novel approach that blends intelligence with automation to transform enterprise IT operations; and describes the design of ignio™, a cognitive automation platform for enterprises. The author concludes by highlighting the challenges in driving cognitive transformation of enterprise operations and providing some suggestions for embarking upon this journey.

The Impact of Cloud Computing on the IT Support Function

The development of digital technologies has opened up new opportunities for e-learning in higher education. These technologies include cloud computing, which promises a scalable and reliable computing environment for both staff and students. This has not only changed the teaching, learning, and research environment, but also affected the way IT support services must now operate in the university sector. This chapter investigates the adoption of cloud computing in higher education through a case study of a major UK university and focuses on how this has affected the IT support function. The benefits and challenges of implementing cloud computing are explored, using questionnaires and interviews to generate data and analysis. The chapter concludes that cloud migration is a complex undertaking requiring a robust strategy that pays due attention to a wide range of issues, notably security concerns and the need for reskilling and the development of new support roles.

On Minimal Hypersurfaces of a Unit Sphere

Minimal compact hypersurface in the unit sphere Sn+1 having squared length of shape operator A2<n are totally geodesic and with A2=n are Clifford hypersurfaces. Therefore, classifying totally geodesic hypersurfaces and Clifford hypersurfaces has importance in geometry of compact minimal hypersurfaces in Sn+1. One finds a naturally induced vector field w called the associated vector field and a smooth function ρ called support function on the hypersurface M of Sn+1. It is shown that a necessary and sufficient condition for a minimal compact hypersurface M in S5 to be totally geodesic is that the support function ρ is a non-trivial solution of static perfect fluid equation. Additionally, this result holds for minimal compact hypersurfaces in Sn+1, (n>2), provided the scalar curvature τ is a constant on integral curves of w. Yet other classification of totally geodesic hypersurfaces among minimal compact hypersurfaces in Sn+1 is obtained using the associated vector field w an eigenvector of rough Laplace operator. Finally, a characterization of Clifford hypersurfaces is found using an upper bound on the integral of Ricci curvature in the direction of the vector field Aw.

An experimental study of the femoral nerve in the long-term periods after modeling lateral interbody spondylodesis of the lumbar spine

Neuropathies of the lumbar plexus trunks, in particular those of the femoral nerve, are the most common complications of lateral interbody spondylodesis of the lumbar spine. Modeling of this surgical intervention in normal animals experimentally makes it possible to assess the degree of its trauma to the nervous structures, and to understand what is the reason for the persistence or aggravation of neurological symptoms iatrogenic injuries or the existing pathology progression. Purpose of the Study. To study histological and morphometric changes in the femoral nerve in the long-term periods after modeling of the lateral interbody spondylodesis of the canine lumbar spine. Design of the Study. An experimental prospective continuous uncontrolled study. Material and Methods. Discectomy via lateral approach was performed in 18 mongrel dogs (aged 2-3 years, mass 13.2-17.6 kg) at the level of L4-5 и L5-6, interbody titanium implants were mounted, the lumbar spine was stabilized with a wire device for external fixation within 30 days. Clinical-and-neurological evaluation was performed, as well as histological investigation of the femoral nerves from the side of surgical approach. Results. In the early postoperative period a temporary decrease in the femoral nerve function was observed, which was manifested by the disorder of the support function and muscle weakness of the pelvic limbs, decrease in the knee reflex, the foot support shift to the metatarsal pad. Later, until the end of the study (18 months), the general condition of all animals was satisfactory, there were no disorders of the limb support function and motor reflexes. After six months, in the femoral nerve there was 4-fold decrease in the proportion of large fast-conducting myelin fibers D 10 m and 3-fold increase in that of the small ones. The mean axon diameter and myelin thickness were 62% and 53% of the norm. After 12-18 months, the dimensional characteristics of myelin fibers were restored. During the entire experiment, 4-6% of myelin fibers were reactively-and-destructively altered. Conclusions. The modeling of the lateral interbody spondylodesis of the lumbar spine in normal animals experimentally demonstrated the absence of neurological symptoms after 6-18 months, which indicated low invasiveness of the surgical intervention. Nevertheless, the subclinical reactive-and-destructive changes in the myelin fibers of the femoral nerve revealed 6 months after the surgery indicated the need for preventive anti-neurotic therapy.

Hyperleukocytic Acute Leukemia Circulating Exosomes Regulate HSCs and BM-MSCs

Hyperleukocytic acute leukemia (HLAL) circulating exosomes are delivered to hematopoietic stem cells (HSCs) and bone marrow mesenchymal stem cells (BM-MSCs), thereby inhibiting the normal hematopoietic process. In this paper, we have evaluated and explored the effects of miR-125b, which is carried by HLAL-derived exosomes, on the hematopoietic function of HSCs and BM-MSCs. For this purpose, we have isolated exosomes from the peripheral blood of HLAL patients and healthy volunteers. Then, we measured the level of miR-125b in exosomes cocultured exosomes with HSCs and BM-MSCs. Moreover, we have used miR-125b inhibitors/mimic for intervention and then measured miR-125b expression and colony forming unit (CFU). Apart from it, HSC and BM-MSC hematopoietic-related factors α-globulin, γ-globulin, CSF2, CRTX4 and CXCL12, SCF, IGF1, and DKK1 expression were measured. Evaluation of the miR-125b and BAK1 targeting relationship, level of miR-125b, and expression of hematopoietic-related genes was performed after patients are treated with miR-125b mimic and si-BAK1. We have observed that miR-125b was upregulated in HLAL-derived exosomes. After HLAL-exosome acts on HSCs, the level of miR-125b is upregulated, reducing CFU and affecting the expression of α-globulin, γ-globulin, CSF2, and CRCX4. For BM-MSCs, after the action of HLAL-exo, the level of miR-125b is upregulated and affected the expression of CXCL12, SCF, IGF1, and DKK1. Exosomes derived from HLAL carry miR-125b to target and regulate BAK1. Further study confirmed that miR-125b and BAK1mimic reduced the expression of miR-125b and reversed the effect of miR-125b mimic on hematopoietic-related genes. These results demonstrated that HLAL-derived exosomes carrying miR-125b inhibit the hematopoietic differentiation of HSC and hematopoietic support function of BM-MSC through BAK1.

CHOICE OF REVASCULARIZATION TECHNIQUE IN PATIENTS WITH ISCHEMIC DIABETIC FOOT

Background Ischemic diabetic foot is determined by trophic disorders of the foot due to a combination of atherosclerosis of the arteries and diabetic lesions. In the United States and some European countries, among major non-traumatic amputations, amputations in patients with diabetes are 45-70%. The use of revascularization can significantly improve the results of treatment of patients with diabetic foot. Features of ischemic diabetic foot require a separate approach to revascularization. There are no generally accepted guidelines for revascularization in diabetic foot in the world today. The choice of revascularization technique remains an open question. The aim of the study. To analyze the effectiveness of differentiated application of intervention techniques of revascularization for the treatment of ischemic diabetic foot. Steps of differentiated choice of revascularization We identified seven steps: determination of indications for revascularization, determination of the critical arterial segment. the level of hemodynamic compensation, determination of the feasibility of revascularization, the choice of revascularization technique, the perform revascularization, the active postoperative monitoring. Materials and methods Diabetic ischemic foot was diagnosed in 133 observations. 123 revascularizations of 94 lower extremities were performed in 91 patients with ischemic diabetic foot. Patients underwent angioplasty, surgical revascularization or hybrid intervention. Results Revascularization was performed in revascularization was performed in 92,4% of patients with ischemic diabetic foot. Amputation-free survival was noted in 85.4% of cases, wound-healing in 62.6%, preservation of foot support function in 79.7%, avoidance of repeated interventions in 78.9%. 5 (5.5%) patients died, 2 of them (2.2:%) within 30 days after revascularization. Conclusions: Differentiated choice of revascularization technique allows to increase the number of patients to be revascularized 92,4%, to reach of the level amputation-free survival to 85,4%, to reach of the level wound-healing to 62,6%, to salvage of foot support function to 79,7%, to perform revascularizations in patients with a high probability of limb amputation.

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

This article introduces the concept of weak sharp minima (WSM) for convex interval-valued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of gHdirectional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of I(R) n and gH-subdifferentiability for convex IVFs. Further, we develop the required gH-subdifferential calculus for convex IVFs. Thereafter, by using the proposed gH-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.