Minimal Rigidity Research Articles

Generic combinatorial rigidity of periodic frameworks

We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell–Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms.To prove our rigidity theorem we introduce and develop periodic direction networks and Z2-graded-sparse colored graphs.

Combinatorics and the rigidity of CAD systems

We study the rigidity of body-and-cad frameworks which capture the majority of the geometric constraints used in 3D mechanical engineering CAD software. We present a combinatorial characterization of the generic minimal rigidity of a subset of body-and-cad frameworks in which we treat 20 of the 21 body-and-cad constraints, omitting only point–point coincidences. While the handful of classical combinatorial characterizations of rigidity focus on distance constraints between points, this is the first result simultaneously addressing coincidence, angular, and distance constraints. Our result is stated in terms of the partitioning of a graph into edge-disjoint spanning trees. This combinatorial approach provides the theoretical basis for the development of deterministic algorithms (that will not depend on numerical methods) for analyzing the rigidity of body-and-cad frameworks.

Body-and-cad geometric constraint systems

Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the body-and-cad structure, composed of rigid bodies in 3D constrained by pairwise coincidence, angular and distance constraints. We identify 21 relevant geometric constraints and develop the corresponding infinitesimal rigidity theory for these structures. The classical body-and-bar rigidity model can be viewed as a body-and-cad structure that uses only one constraint from this new class.As a consequence, we identify a new, necessary, but not sufficient, counting condition for minimal rigidity of body-and-cad structures: nested sparsity. This is a slight generalization of the well-known sparsity condition of Maxwell.

Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterization of the graphs that admit a realization as a minimally rigid generic bar-joint framework in $\mathbb{R}^2$. A more general theory is developed for frameworks in $\mathbb{R}^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\mathcal{M}$. Furthermore, when $\mathcal{M}$ is a union of concentric spheres, or a union of parallel planes, or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.

Relation between the moments of inertia of the leading and driven parts of the composite flywheel with a torsional damper

This article considers the results of investigation of the effect of parameters of the torsional damper of a composite flywheel on the amplitude of torque on the primary shaft of a gearbox. It is shown that it is reasonable to install a torsional damper with minimal rigidity.

Deriving Finite Sphere Packings

Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for deriving all packings of n spheres in R^3 satisfying minimal rigidity constraints (>= 3 contacts per sphere and >= 3n-6 total contacts). We derive such packings for n <= 10, and provide a preliminary set of maximal contact packings for 10 < n <= 20. The resultant set of packings has some striking features, among them: (i) all minimally rigid packings for n <= 9 have 3n-6 contacts, (ii) non-rigid packings satisfying minimal rigidity constraints arise for n >= 9, (iii) the number of ground states (i.e. packings with the maximal number of contacts) oscillates with respect to n, (iv) for 10 <= n <= 20 there are only a small number of packings with the maximal number of contacts, and for 10 <= n < 13 these are all commensurate with the HCP lattice. The general method presented here may have applications to other related problems in mathematics, such as the Erdos repeated distance problem and Euclidean distance matrix completion problems.

Statics and dynamics of the wormlike bundle model

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F -actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink-induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity.

Minimal Energy Clusters of Hard Spheres with Short Range Attractions

We calculate the ground states of hard-sphere clusters, in which n identical hard spherical particles bind by isotropic short-ranged attraction. Combining graph theoretic enumeration with basic geometry, we analytically solve for clusters of n<or=10 particles satisfying minimal rigidity constraints. For n<or=9 the ground state degeneracy increases exponentially with n, but for n>9 the degeneracy decreases due to the formation of structures with >3n-6 contacts. Interestingly, for n=10 and possibly at n=11 and n=12, the ground states of this system are subsets of hexagonal close-packed crystals. The ground states are not icosahedra at n=12 and n=13. We relate our results to the structure and thermodynamics of suspensions of colloidal particles with short-ranged attractions.

Formation Reorganization by Primitive Operations on Directed Graphs

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we study the construction and transformation of 2-D persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. Both notions are currently being used in various studies on coordination and control of autonomous multiagent formations. In the context of mobile autonomous agent formations, persistence characterizes the efficacy of a directed formation structure with unilateral distance constraints seeking to preserve the shape of the formation. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequentially build any minimally persistent graph (i.e., persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the online reorganization of the sensing and control architecture of an autonomous agent formation. We prove that we can obtain any minimally persistent formation from any other one by a sequence of elementary local operations such that minimal persistence is preserved throughout the reorganization process. Finally, we briefly explore how such transformations can be performed in a decentralized way. </para>

Use of Intravenous Valproate in a Patient With Neuroleptic Malignant Syndrome

Back to table of contents Previous article Next article LetterFull AccessUse of Intravenous Valproate in a Patient With Neuroleptic Malignant SyndromeRahul R. Tadke, M.D., DNB, and Praveen Suryavanshi, MBBS, DPMRahul R. TadkeSearch for more papers by this author, M.D., DNB, and Praveen SuryavanshiSearch for more papers by this author, MBBS, DPMPublished Online:1 Feb 2006AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail SIR: A 22-year-old woman was admitted through casualty, with a history of altered behavior for approximately 15 days and history of fever, rigidity, tremors, and one episode of incontinence for a few days. The patient had autonomic disturbances, was partly oriented to time and place, and general condition was moderate.History given by a close relative about cheerfulness, excessive talkativeness, singing songs, reduced need for sleep, and grandiose ideation for approximately 2 weeks indicated an episode of mania. The patient received an injection of haloperidol intramuscularly to control the behavior a few days before, prior to the onset of new symptoms.A clinical diagnosis of neuroleptic malignant syndrome (NMS) was made, although other differentials of delirium due to general medical condition, including meningitis, were also considered.Baseline investigations were within normal limits, and total leukocytes count of 9000/cmm and the CSF study was inconclusive. Serum creatinine phosphokinase (CPK) levels were 3850 U/liter, suggestive of N.M.S. and this confirmed the diagnosis.Injection valproate was administered intravenously 250 mg on the first day and then 250 mg 12 hourly from the next day. A clonazepam tablet was also administered when needed. The following day, dramatic improvement in this patient, was observed. She was well oriented to time, place and person, and the rigidity had markedly reduced. Tremors were minimal, and there was no fever. After 6 days, the patient had minimal rigidity and mild tremors. There were no behavioral disturbances barring mild euphoria.Repeat serum CPK levels after 10 days was 30 U/liter (well within normal limits) and other baseline investigations were within normal limits. The patient was later switched to oral sodium valproate, and there were no features of NMS. The serum valproate level was 87 mcg/ml after 2 weeks.Intravenous valproate has been used for catatonia.1 In this isolated case (by chance), intravenous valproate was found to be effective in the symptoms of NMS.2,3There was no fear of the reemergence of psychotic features, which is common with bromocriptine. The strict monitoring as required for bromocriptine was also not needed. It serves a dual purpose for controlling manic features in patients of bipolar disorder.4 Even a substitute novel (atypical) antipsychotic (although less) carries the risk of NMS.Panjabrao Deshmukh Medical College , Department of Psychiatry, Amravati , Maharashtra, IndiaReferences1 Kruger S, Braunig P: Intravenous valproic acid in the treatment of severe catatonia J Neuropsychiatry Clin Neurosci. 2001; 13(2):303-304Google Scholar2 Lauterbach EC: Valproate for catatonia: need for caution in patients on SSRIs and antipsychotics.: J Neuropsychiatry Clin Neurosci. 2002;14(1):84-86Google Scholar3 Spehlmann R, Norcross K, Rasmus SC, et al: Improvement of stiff-man syndrome with sodium valproate. Neurology. 1981; 31(9):1162-113Google Scholar4 Grunze H, Erfurth A, Amann B, et al: Intravenous valproate loading in acutely manic and depressed bipolar I patients. J Clin Psychopharmacol 1999; 19(4):303–309Crossref, Medline, Google Scholar FiguresReferencesCited byDetailsCited ByNeuroleptic Malignant Syndrome19 July 2016 | Annals of Pharmacotherapy, Vol. 50, No. 11Comment: Neuroleptic Malignant Syndrome Versus Serotonin Syndrome: The Search for a Diagnostic Tool13 March 2012 | Annals of Pharmacotherapy, Vol. 46, No. 4Neuroleptic Malignant Syndrome Following Levomepromazine DiscontinuationHisashi TaniiM.D., Ph.D.,Keiichi SakaM.D.,Ken InoueM.D., Ph.D.,Motohiro OkadaM.D., Ph.D.,1 April 2010 | The Journal of Neuropsychiatry and Clinical Neurosciences, Vol. 22, No. 2 Volume 18Issue 1 February 2006Pages 131-132 Metrics PDF download History Published online 1 February 2006 Published in print 1 February 2006

Effects of sildenafil citrate on ejaculation latency, detumescence time, and refractory period: Placebo-controlled, double-blind, crossover laboratory setting study

To evaluate whether sildenafil citrate (SC) prolongs ejaculation latency and detumescence time and shortens the refractory period in a laboratory setting. Two successive double-blind, placebo-controlled, crossover laboratory studies were performed with 30 different healthy volunteers in each study (total of 60). In the first study, the subject ingested placebo or SC. Real-time penile tumescence and rigidity monitoring and audiovisual sexual stimulation was performed. When the subject had his best erection, he applied vibratory stimulation until he ejaculated, and then audiovisual sexual stimulation was stopped. Monitoring was continued until he lost rigidity. The test was repeated with the second medication in 7 to 15 days. In the second study, another group of 30 volunteers were tested, as in the first study, and audiovisual sexual stimulation was continued for an additional hour after ejaculation. In the first study, the time to ejaculation with vibratory stimulation was 2.23 and 3.89 minutes (P = 0.01) and the time to minimal tip rigidity after ejaculation was 1.93 and 3.1 minutes (P <0,001) in the placebo and SC groups, respectively. In the second study, the time to ejaculation with vibratory stimulation was 2.23 and 4.91 minutes (P = 0.006), the time to best tip rigidity after ejaculation was 19.10 and 15.66 minutes (P = 0.242), and the area under the curve of tip rigidity in 3 minutes after ejaculation was 73.61 and 144.05 (P <0.001) in the placebo and SC groups, respectively. In this laboratory setting, SC seemed to prolong the ejaculation latency time. The detumescence time was also longer, with better quality. However, we did not show that SC shortens the refractory period after ejaculation.

QSAR modeling on binding affinity of diverse estrogenic flavonoids: electronic, topological and spatial functions in quantitative approximation

Phytoestrogens have been explored as promising next generation estrogenic drug candidates with minimum cardiovascular risks. Investigating spatial, electronic and topological properties of the molecules, structure-activity relationships were drawn in an endeavor to find out the basic pharmacophore features of flavonoids for binding with the estrogen receptor. Implementing multi-parameter linear regression analysis, a significant relationship ( R 2=0.892 and Q 2=0.805 for n=19) was established that explained 86.097% variance in binding affinity to the receptor. This study revealed the importance of partial charges at atoms C 2′ and C 4′ in the phenyl ring C, electrotoplogical state of atom C 7 in the phenyl ring A and the molecular orientation and conformational stringency factors. It has been found that substitution by an e − donating group in the phenyl ring at C 2′, e − withdrawing groups at C 4′ and C 7 of the molecule in conjunction with minimal conformational rigidity could be important for estrogenic activity.

Clinical efficacy of sildenafil in primary pulmonary hypertension. A randomized, placebo-controlled, double-blind, crossover study

To evaluate whether sildenafil citrate (SC) prolongs ejaculation latency and detumescence time and shortens the refractory period in a laboratory setting.Two successive double-blind, placebo-controlled, crossover laboratory studies were performed with 30 different healthy volunteers in each study (total of 60). In the first study, the subject ingested placebo or SC. Real-time penile tumescence and rigidity monitoring and audiovisual sexual stimulation was performed. When the subject had his best erection, he applied vibratory stimulation until he ejaculated, and then audiovisual sexual stimulation was stopped. Monitoring was continued until he lost rigidity. The test was repeated with the second medication in 7 to 15 days. In the second study, another group of 30 volunteers were tested, as in the first study, and audiovisual sexual stimulation was continued for an additional hour after ejaculation.In the first study, the time to ejaculation with vibratory stimulation was 2.23 and 3.89 minutes (P = 0.01) and the time to minimal tip rigidity after ejaculation was 1.93 and 3.1 minutes (P <0,001) in the placebo and SC groups, respectively. In the second study, the time to ejaculation with vibratory stimulation was 2.23 and 4.91 minutes (P = 0.006), the time to best tip rigidity after ejaculation was 19.10 and 15.66 minutes (P = 0.242), and the area under the curve of tip rigidity in 3 minutes after ejaculation was 73.61 and 144.05 (P <0.001) in the placebo and SC groups, respectively.In this laboratory setting, SC seemed to prolong the ejaculation latency time. The detumescence time was also longer, with better quality. However, we did not show that SC shortens the refractory period after ejaculation.

Minimal Lyapunov exponents, quasiconformal structures, and rigidity of non-positively curved manifolds

For a closed irreducible non-positively curved manifold M, we show that if at almost every point one of the positive Lyapunov exponents for the geodesic flow achieves the minimum allowed by the curvature, then M is locally symmetric of non-compact type. Among the applications of this result, we show that rank one symmetric spaces may be characterized among negatively curved Hadamard manifolds admitting a cocompact lattice solely by the quasiconformal structure and Hausdorff dimension of their ideal boundary. We also prove a rigidity result for semiconjugacies.

Minimal Entropy Rigidity for Lattices in Products of Rank One Symmetric Spaces

where B(x,R) is the ball of radius R around a fixed point x in the universal cover X. (For noncompact M , see Section 6.2.) The number h(g) is independent of the choice of x, and equals the topological entropy of the geodesic flow on (M, g) when the curvature K(g) satisfies K(g) ≤ 0 (see [Ma]). Note that while the volume Vol(M, g) is not invariant under scaling the metric g, the normalized entropy

Minimal entropy rigidity for foliations of compact spaces

We formulate and prove a foliated version of a theorem of Besson, Courtois, and Gallot establishing the minimal entropy rigidity of negatively curved locally symmetric spaces. One corollary is a foliated version of Mostow’s rigidity theorem.

Gamma knife subthalamotomy for Parkinson disease: the subthalamic nucleus as a new radiosurgical target

✓ The authors present the neuroimaging, treatment planning, and radiosurgical technique for the first reported case of unilateral radiosurgical subthalamotomy, which was performed to control motor symptoms associated with advanced Parkinson disease (PD) in a patient who had undergone previous contralateral radiofrequency (RF) pallidotomy. A 73-year-old woman with end-stage PD had undergone RF pallidotomy of the right globus pallidus with resolution of symptoms. Two years following this procedure, due to the natural progression of her disease, she suffered recurrent motor fluctuations, dyskinesia, and worsening bradykinesia of the right side. Her Parkinson's Disease Disability Rating (PDDR) score was 28. Computerized tomography and magnetic resonance (MR) imaging were used to localize the left subthalamic nucleus (STN). The patient underwent gamma knife radiosurgery—a single shot of 120 Gy was administered using the 4-mm collimator helmet. The patient was evaluated up to 42 months after the procedure. The dyskinesia became minimal. Right-sided motor control improved as did her balance. At 3 months after treatment MR imaging demonstrated the radiosurgical lesion in the left STN. At 3.5 years postradiosurgery, she experienced minimal focal (oral) dyskinesia, no bradykinesia or rigidity, and her PDDR score was 11. Radiosurgery of the STN in this case was safe and effective. The STN is a readily localized anatomical target with neuroimaging. Radiosurgery avoids the risks of open procedures.

Carotid-cavernous fistula after partial maxillectomy: Case report

An otherwise healthy 18-year-old white man underwent a right partial maxillectomy for treatment of an osteoblastoma, which included the maxilla from the first premolar posteriorly and included the pterygoid plates. The operation was uneventful except for the unplanned inclusion in the resection of a less than 1 cm segment of the floor of the middle cranial fossa at the superior aspect of the medial pterygoid plate. No cerebrospinal fluid (CSF) leak or other evidence of dural perforation were noted. The immediate postoperative course was uneventful, and the patient was discharged the day after surgery. The patient returned 5 days later, reporting discomfort associated with his left eye, double vision, nausea, and vomiting. He also reported postoperative sinus congestion on the right, which had resulted in his blowing his nose “a lot.” He denied any fever or chills. On presentation, he was afebrile, and his vital signs were within normal limits. The expected amount of postoperative right facial swelling was present. His pupils were equal, round, and reactive to light and accommodation. The extraocular movements were intact, with the exception of the complete inability to abduct the left eye (Fig 1). There was mild chemosis and minimal edema of the left upper and lower eyelids, without discoloration and injection of the sclera. Funduscopic examination was normal, and visual acuity was 20/40. There was no lymphadenopathy, and the remainder of the physical examination was unremarkable. Laboratory values were significant only for a white blood cell count of 12,400 cm, with a normal differential count. A computed tomography (CT) scan was obtained which, in addition to the expected surgical defect, showed air-fluid levels in the right ethmoid and maxillary sinuses and the sphenoid sinuses bilaterally. The sphenoid sinuses were noted to be large. There was also moderate venous engorgement around the left globe, but no retrobulbar swelling. Additionally, there was enhancement adjacent to the left cavernous sinus and extradural air in the right temporal region. The patient was admitted to the hospital with a presumptive diagnosis of early left cavernous sinus thrombosis and started on ampicillin-sulbactam, morphine, and aspirin. On the first hospital day, he developed increased pain behind the left eye along with proptosis (6 mm) of the left globe (Fig 2). In addition, he began complaining of some neck stiffness andwas found to have minimal nuchal rigidity. Neurosurgery and infectious disease consults were obtained. There was concern that the patient had sinusitis, and was developing an early meningitis; therefore, ceftriaxone was added to his antibiotic regimen. A magnetic resonance imaging (MRI) scan was obtained, which showed flow through the cavernous sinuses along with a small amount of blood in the epidural and subdural spaces. An incidental finding was a cerebral vascular malformation in the left occipital area. At this point, the presumptive diagnosis was inflammation of the dura and sphenoid sinusitis. Steroids were considered, but withheld in view of a possible infectious cause. On the second hospital day, the physical findings were unchanged, and the white blood count had decreased to 11,600 cm. The ampicillin-sulbactam was stopped, and clindamycin was started. On the third hospital day, the patient claimed the discomfort associated with his left eye was less severe, but his physical findings remained unchanged. However, the following day, he began complaining of left forehead numbness and decreased visual acuity in the left eye. A second CT and MRI were completed, which *Formerly, Dennis A. and Roberta R. Youde Fellow in Head and

Ablative Therapy for Movement Disorders: Does Thalamotomy Alter the Course of Parkinson’s Disease?

Although there is no confirmed evidence that therapy alters the course of Parkinson's disease, some follow-up of patients who have undergone thalamotomy has suggested it might slow or even halt the progress of the disease. A retrospective semiquantitative assessment of 55 patients undergoing bilateral thalamotomy and 31 undergoing unilateral operation confirms the previously held notion that postencephalitic disease or clinical onset below age 40 may progress so slowly as to appear arrested after thalamotomy. Patients left with no tremor and minimal rigidity after completion of unilateral or bilateral surgery, whether their disease is of youthful onset, postencephalitic or not, may also appear to follow stable courses postoperatively. This occurs in patients whose tremor and rigidity have been controlled by bilateral thalamotomy and also in those in whom unilateral tremor and rigidity have been controlled by unilateral surgery in the absence of significant tremor and rigidity on the other side of the body. Possible explanations are discussed.

Direct-current-magnetron deposition of molybdenum and tungsten with rf-substrate bias

It has recently been shown that the stress of many refractory thin films deposited by dc-magnetron sputtering can be influenced by the sputtering pressure. Usually the transition from compressive to tensile stress is too sharp for pressure to be a reliable variable for stress control. This is particularly true in applications such as x-ray optics and lithography where extremely low stress is required owing to minimal substrate rigidity. In this paper, we show that there exists a broad region of the parameter space of current, pressure, and rf-substrate bias where tungsten and molybdenum may be deposited with low stress. A detailed study of the effects of these parameters upon stress, plasma etch rate, and resistivity is reported.